Question 1

Sambhu buys rice at Rs. 10 per kilogram and sets a price that gives a 20 percent profit according to that marked rate. However, his weighing balance is faulty and shows 1000 grams when the true weight is only 800 grams. What is his actual gain perce…

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Introduction / Context: This question combines the idea of profit based on marked price with an error in measurement. Sambhu thinks he is selling one kilogram, but due to a faulty balance he actually gives less rice while still charging the full selling price. This leads to an effective gain percentage that is higher than the marked profit because he is delivering reduced quantity for the same price. Given Data / Assumptions: Cost price of rice is Rs. 10 per true kilogram. He marks the price to earn 20 percent profit. His balance shows 1000 grams when the actual weight is only 800 grams. We assume the marked price is applied on the visible one kilogram reading. We must find his actual gain percentage on the true cost. Concept / Approach: There are two sources of gain. First, he increases the price by 20 percent over the cost price. Second, he gives only 0.8 kilogram of rice when the customer believes they receive 1 kilogram. To compute the true gain, we consider the revenue from the sale corresponding to the price of one displayed kilogram and compare it with the real cost of the actual quantity delivered. The effective cost of 0.8 kilogram is lower than the cost of 1 kilogram, so the overall profit percentage increases. Step-by-Step Solution: True cost price per kilogram is 10 rupees.For a 20 percent profit, the marked selling price per kilogram equals 10 * 1.20 which is 12 rupees.Due to the faulty balance, when the scale shows 1000 grams, the customer actually receives only 800 grams.So for every indicated kilogram sold at 12 rupees, Sambhu gives 0.8 kilogram of rice.The true cost of 0.8 kilogram equals 0.8 * 10 which is 8 rupees.Therefore, profit per indicated kilogram sold equals 12 minus 8 which is 4 rupees.Percentage profit equals 4 divided by 8 multiplied by 100, which is 50 percent. Verification / Alternative check: Another way to see this is to compute effective selling price per true kilogram. Sambhu collects 12 rupees for 0.8 kilogram, so per true kilogram he effectively collects 12 divided by 0.8 which is 15 rupees. Comparing this with his cost price of 10 rupees per kilogram, the profit per kilogram is 5 rupees. The percentage profit is then 5 divided by 10 multiplied by 100 which is again 50 percent. Both methods agree on the same answer, so our calculations are consistent. Why Other Options Are Wrong: Option 25 percent would occur if he only had the marked price profit without any weighing error, which is not the case here. Option 75 percent and 60 percent are higher than the true calculated gain; they would require either a larger markup or an even bigger error in weight. The precise data given in the question leads to exactly 50 percent, making option 50 percent the only correct choice. Common Pitfalls: Some learners forget that the customer actually pays for an indicated kilogram but gets less rice, and they calculate profit using only the 20 percent markup. Others incorrectly treat 0.8 kilogram as 80 percent profit or mix up which quantity is treated as base in the percentage formula. Always identify the true cost of the actual quantity delivered and compare it with the amount collected from the customer to find the real gain percentage. Final Answer: Sambhu actual gain percentage on the transaction is 50 percent.

Question 2

Two shopkeepers sell the same article for the same selling price. The first shopkeeper calculates his profit percentage on the selling price, and the second shopkeeper calculates his profit percentage on the cost price. For both of them the profit p…

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Introduction / Context: This problem highlights an important conceptual difference between profit calculated on selling price and profit calculated on cost price. Even though the numerical percentage is the same, using a different base produces different rupee profits. The question links these two profit amounts through a common selling price and a known difference in rupee profit, and asks for the combined cost prices of both shopkeepers. Given Data / Assumptions: Both shopkeepers sell the article at the same selling price S. First shopkeeper calculates profit as 25 percent of the selling price. Second shopkeeper calculates profit as 25 percent of the cost price. The difference between their profits is Rs. 175. We must find the sum of their cost prices. Concept / Approach: Let the common selling price be S. For the first shopkeeper, profit one equals 25 percent of S, so profit one equals 0.25 * S and his cost price is S minus profit one. For the second shopkeeper, profit two equals 25 percent of his own cost price C2, and selling price S equals C2 plus profit two. Using these relationships, we first express both profits in terms of S, then use the given difference of 175 rupees to find S. After that, we compute each cost price and add them together. Step-by-Step Solution: Let selling price for both be S rupees.First shopkeeper profit P1 equals 25 percent of S, so P1 equals 0.25 * S.His cost price C1 equals S minus P1 equals S minus 0.25 * S equals 0.75 * S.Second shopkeeper profit P2 equals 25 percent of his cost price C2, so P2 equals 0.25 * C2.His selling price S equals C2 plus P2 equals C2 + 0.25 * C2 equals 1.25 * C2, so C2 equals S / 1.25 equals 0.80 * S.Then P2 equals 0.25 * 0.80 * S equals 0.20 * S.The difference between their profits is P1 minus P2 equals 0.25 * S minus 0.20 * S equals 0.05 * S.We are given that this difference is 175 rupees, so 0.05 * S equals 175 and S equals 175 / 0.05 equals 3500 rupees.Now C1 equals 0.75 * 3500 equals 2625 rupees, and C2 equals 0.80 * 3500 equals 2800 rupees.Sum of cost prices equals 2625 plus 2800 which is 5425 rupees. Verification / Alternative check: We can verify by computing individual profits using S equals 3500 rupees. First shopkeeper profit is 25 percent of 3500 which is 875 rupees. Second shopkeeper cost price is 2800 rupees, so his profit is 25 percent of 2800 which is 700 rupees. The difference between these profits is 875 minus 700 equals 175 rupees, which matches the problem condition. This confirms that S and the calculated cost prices are consistent with all the given information. Why Other Options Are Wrong: Any other sum of cost prices would result from taking an incorrect selling price S or misapplying the percentage definitions. For example, if we incorrectly treated both percentages as based on cost price, the profit difference would not match 175 rupees. Similarly, sums like 4875, 4675, or 5275 do not arise from any consistent computation using the given percentages and the same selling price condition. Only 5425 rupees fits the derived equations. Common Pitfalls: One common mistake is to assume that both shopkeepers calculate profit on cost price, which makes the problem trivial and ignores the main concept being tested. Another error is mixing up which variable is the base for each percentage, leading to incorrect equations. Finally, some learners forget that the selling price for both shopkeepers is the same, which is crucial for linking their cost prices. Carefully distinguishing between profit on selling price and profit on cost price is essential here. Final Answer: The sum of the cost prices of the two shopkeepers is Rs. 5425.

Question 3

A rice trader buys 25 quintals of rice for a total of Rs. 1825. During transportation, 27 percent of the rice is lost. At what selling price per quintal should he sell the remaining rice in order to earn a profit of 20 percent on his total investmen…

Accepted Answer

Introduction / Context: This question involves both loss of quantity and profit on cost, a situation that appears frequently in commercial aptitude problems. The trader loses a certain percentage of the physical quantity during transportation, but wants to maintain a target overall profit on the total money invested. We must therefore work with total cost, remaining quantity, and required selling price per unit to reach the desired profit. Given Data / Assumptions: Total quantity bought is 25 quintals. Total cost price is Rs. 1825. Loss in transportation is 27 percent of the quantity. Target profit on total cost is 20 percent. We must find the required selling price per quintal for the remaining rice. Concept / Approach: The main steps are: first, compute the quantity of rice remaining after the transportation loss. Second, calculate the required total revenue to achieve a 20 percent profit on the initial cost. Finally, divide this required total revenue by the remaining quantity to get the required selling price per quintal. It is very important to realize that the profit percentage is calculated on the original cost, regardless of the quantity lost. Step-by-Step Solution: Total cost price equals 1825 rupees.Initial quantity equals 25 quintals.Loss in transportation is 27 percent, so remaining quantity equals 73 percent of 25 quintals.Remaining quantity equals 0.73 * 25 which is 18.25 quintals.To earn a profit of 20 percent on the cost, total revenue required equals 1.20 * 1825.Compute required revenue as 1.20 * 1825 which is 2190 rupees.Required selling price per quintal equals total required revenue divided by remaining quantity, that is 2190 / 18.25.2190 divided by 18.25 equals 120 rupees per quintal. Verification / Alternative check: We can verify by checking the actual profit at this selling price. Selling 18.25 quintals at Rs. 120 per quintal yields 18.25 * 120 which is 2190 rupees in total. Profit equals 2190 minus 1825 which is 365 rupees. Percentage profit equals 365 divided by 1825 multiplied by 100, which is exactly 20 percent. Therefore, the selling price of 120 rupees per quintal satisfies the condition for the desired profit even after the transportation loss. Why Other Options Are Wrong: At 44.4 rupees per quintal, the total revenue would be far below the cost, leading to a loss rather than a profit. At 87.6 rupees per quintal or 115.8 rupees per quintal, the total revenue would not reach 2190 rupees and thereby would not provide a full 20 percent profit on 1825 rupees. Only 120 rupees per quintal gives the exact required total revenue to achieve the target profit. Common Pitfalls: Some learners incorrectly calculate the 20 percent profit on the reduced quantity instead of the original cost, which changes the base incorrectly. Others forget to adjust the quantity after the 27 percent loss and simply divide the required revenue by the original 25 quintals. It is crucial to separate the concepts: profit is on cost, while selling price per quintal depends on how much quantity is left for sale after losses in transportation. Final Answer: The trader should sell the remaining rice at Rs. 120 per quintal to earn a 20 percent profit on his investment.

Question 4

A shopkeeper allows a discount of 25 percent on the marked price of an article and, at that discounted selling price, he suffers a loss of 15 percent. What would be his profit percentage if he sells the article at the full marked price without any d…

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Introduction / Context: This question connects discount, loss, and profit. The shopkeeper initially gives a discount on the marked price and ends up making a loss. We must then determine what would happen if he did not give any discount and sold at the full marked price. This involves relating marked price, selling price after discount, cost price, and then recalculating profit when selling at the marked price. Given Data / Assumptions: Discount on marked price is 25 percent. At the discounted price, there is a loss of 15 percent. The cost price remains the same in both scenarios. We must compute the profit percentage if the article is sold at marked price. Percentages are with respect to cost price when speaking of profit or loss. Concept / Approach: Let the marked price be M. The discount of 25 percent means the selling price with discount is 75 percent of M. This discounted selling price produces a loss of 15 percent, so it must be 85 percent of the cost price C. Using these relationships, we can express cost price in terms of the marked price. Then we can compute profit when selling at the full marked price M by comparing M with C, using the standard profit percentage formula. Step-by-Step Solution: Let marked price be M rupees.After 25 percent discount, selling price S1 equals 0.75 * M.This S1 corresponds to a loss of 15 percent, so S1 equals 0.85 * C where C is the cost price.Therefore 0.75 * M equals 0.85 * C.Cost price C equals (0.75 / 0.85) * M.Now consider selling at full marked price M. Profit then equals M minus C.Substitute C: profit equals M minus (0.75 / 0.85) * M.So profit equals M * (1 minus 0.75 / 0.85) which simplifies to M * ((0.85 minus 0.75) / 0.85) equals M * (0.10 / 0.85).Profit percentage equals (profit divided by C) * 100 which simplifies to (0.10 / 0.75) * 100, approximately 13.33 percent. Verification / Alternative check: We can choose a convenient value for the marked price to verify. Let M equal 100 rupees. Then discounted selling price S1 equals 75 rupees. If this is 85 percent of C, then C equals 75 / 0.85 which is about 88.24 rupees. Profit at full marked price is 100 minus 88.24 equals 11.76 rupees. The profit percentage is 11.76 divided by 88.24 multiplied by 100, which is about 13.33 percent. This numerical verification agrees with the algebraic result. Why Other Options Are Wrong: Value 11.76 is the profit in rupees from the example with M equal to 100, not the profit percentage. Options 12.12 and 14.28 percent arise from misplacing terms when simplifying ratios or from using the wrong base in percentage calculations. Only 13.33 percent correctly captures the ratio of profit to cost price when the article is sold at the full marked price. Common Pitfalls: Many learners confuse which amount is considered as base for different percentages. Loss percentage is based on cost price, while discount percentage is based on marked price. Another common mistake is to subtract or add percentages directly without translating them into actual amounts relative to a chosen base. Setting up equations systematically with variables M and C and then simplifying is the safest method to avoid these errors. Final Answer: If the article is sold at the full marked price, the shopkeeper makes a profit of approximately 13.33 percent.

Question 5

The profit obtained on selling an article for Rs. 540 is exactly equal to the loss incurred when the same article is sold for Rs. 370. If the article is instead sold for Rs. 910, what will be the profit percentage?

Accepted Answer

Introduction / Context: This question uses a symmetric situation where the profit at a higher selling price equals the loss at a lower selling price. The same cost price is involved in both cases. From this symmetry we can determine the cost price and then compute the profit percentage when the article is sold at a new, higher selling price. It is a standard and elegant type of profit and loss problem. Given Data / Assumptions: Selling price one is Rs. 540 and results in a profit. Selling price two is Rs. 370 and results in a loss. Magnitude of profit at 540 rupees equals magnitude of loss at 370 rupees. The cost price is the same in all cases. Selling price three is Rs. 910 and we must find the profit percentage at this price. Concept / Approach: Let the cost price be C. At selling price 540, profit equals 540 minus C. At selling price 370, loss equals C minus 370. The problem states that these magnitudes are equal, so we set 540 minus C equal to C minus 370 and solve for C. Once we know C, we compute profit at 910 rupees as 910 minus C and then express this as a percentage of C by using the standard profit percentage formula. Step-by-Step Solution: Let cost price be C rupees.At selling price 540, profit P1 equals 540 minus C.At selling price 370, loss L1 equals C minus 370.Given that profit equals loss in magnitude, we have 540 minus C equals C minus 370.Rearranging gives 540 plus 370 equals 2C.So 910 equals 2C and therefore C equals 455 rupees.Now consider selling price 910 rupees.Profit at 910 equals 910 minus 455 which is 455 rupees.Profit percentage equals 455 divided by 455 multiplied by 100 which equals 100 percent. Verification / Alternative check: We can verify the equal profit and loss condition using cost price 455 rupees. At 540 rupees, profit equals 540 minus 455 equals 85 rupees. At 370 rupees, loss equals 455 minus 370 which is also 85 rupees. Thus, the given statement of equal magnitude is satisfied. At 910 rupees, selling price is exactly double the cost price, which naturally leads to a profit equal to the cost price and therefore a 100 percent profit. This consistent reasoning confirms the result. Why Other Options Are Wrong: Profit percentages 25, 33, and 50 percent would correspond to much smaller profits relative to the cost price. For instance, a 50 percent profit would require a profit of only half of 455, that is about 227.5 rupees, which is far less than the actual profit of 455 rupees at a selling price of 910. Since the selling price is exactly twice the cost price, the only correct profit percentage is 100 percent. Common Pitfalls: Some learners incorrectly average the two selling prices and treat their difference from the cost price as profit. Others misinterpret the condition by equating profit percentages instead of profit amounts. The correct approach is to equate the rupee profit and rupee loss magnitudes, form a simple linear equation, and solve for the cost price. Once that is clear, the calculation of the new profit percentage is straightforward. Final Answer: When the article is sold for Rs. 910, the profit percentage is exactly 100 percent.

Question 6

A trader has 22 quintals of wheat. He sells part of it at a profit of 23 percent and the remaining part at a profit of 33 percent, so that his overall profit on the entire 22 quintals is 27 percent. How many kilograms of wheat are sold at the 33 per…

Accepted Answer

Introduction / Context: This question involves a weighted average of profit percentages. A trader sells different portions of a commodity at two different profit rates and the overall profit percentage on the entire quantity is given. The task is to determine how much of the commodity was sold at one of the profit rates. This is a classic application of the concept of weighted averages and linear equations in profit and loss problems. Given Data / Assumptions: Total wheat quantity is 22 quintals. Part of the wheat is sold at 23 percent profit. The remaining part is sold at 33 percent profit. Overall profit on the entire 22 quintals is 27 percent. We must find the quantity sold at 33 percent profit, expressed in kilograms. Concept / Approach: Since the profit percentages differ on different parts of the quantity but the cost price per quintal is uniform, we can assume a convenient cost price per quintal, for example Rs. 1, to simplify the algebra. Let x quintals be sold at 23 percent profit and the remaining 22 minus x at 33 percent profit. We then compute the total revenue using these profit rates, set it equal to the revenue that would correspond to a uniform 27 percent profit on all 22 quintals, and solve the resulting linear equation for x. Finally we convert the quantity that corresponds to 33 percent profit into kilograms. Step-by-Step Solution: Assume cost price per quintal equals 1 rupee for simplicity.Total cost price for 22 quintals equals 22 rupees.Let x quintals be sold at 23 percent profit, so selling price for these is x * 1.23.Remaining quantity equals 22 minus x quintals, sold at 33 percent profit, giving selling price (22 minus x) * 1.33.Total selling price from both parts equals x * 1.23 plus (22 minus x) * 1.33.Overall profit is 27 percent on 22 rupees, so total selling price should also equal 22 * 1.27 equals 27.94 rupees.Set x * 1.23 + (22 minus x) * 1.33 equal to 27.94 and simplify.Expanding gives 1.23x + 29.26 minus 1.33x equals 27.94.This simplifies to minus 0.10x + 29.26 equals 27.94.So minus 0.10x equals minus 1.32, and x equals 13.2 quintals.Therefore, quantity sold at 33 percent profit equals 22 minus 13.2 equals 8.8 quintals.One quintal is 100 kilograms, so 8.8 quintals equals 8.8 * 100 equals 880 kilograms. Verification / Alternative check: We can verify quickly. Revenue from 13.2 quintals at 23 percent profit is 13.2 * 1.23 equals 16.236 rupees. Revenue from 8.8 quintals at 33 percent profit is 8.8 * 1.33 equals 11.704 rupees. Total revenue equals 16.236 plus 11.704 equals 27.94 rupees. With total cost price 22 rupees, profit is 5.94 rupees and profit percentage is 5.94 divided by 22 times 100 which is 27 percent. This matches the required overall profit and confirms that 8.8 quintals, or 880 kilograms, were sold at 33 percent profit. Why Other Options Are Wrong: 1320 kilograms correspond to 13.2 quintals, which is the quantity sold at 23 percent profit, not 33 percent profit. Values 440 kilograms and 1760 kilograms do not satisfy the weighted average equation and would not produce an overall profit of 27 percent. Only 880 kilograms results in a combined selling price that matches the required average profit on the entire stock. Common Pitfalls: Some learners try to average the percentages directly using proportions of profit rates alone, without considering the total quantity. Others mix up which part of the quantity corresponds to each profit rate when interpreting the algebraic solution. Using a clear variable definition, writing out the full total selling price expression, and checking units carefully helps avoid these mistakes. Final Answer: The trader sells 880 kilograms of wheat at a profit of 33 percent.

Question 7

In a certain business, the profit is 220 percent of the cost price. If the cost price increases by 25 percent but the selling price remains unchanged, then approximately what percentage of the selling price does the new profit represent?

Accepted Answer

Introduction / Context: This question relates profit to both cost price and selling price, and examines what happens when the cost price changes but the selling price does not. Initially the profit is very high relative to cost. After a cost increase, the absolute profit falls even though the selling price is unchanged. The problem asks us to express the new profit as a percentage of the selling price, which is a slightly different base than usual. Given Data / Assumptions: Initial profit is 220 percent of cost price. Cost price then increases by 25 percent. Selling price remains the same as before. We must find what percentage of the selling price the new profit is, approximately. All prices are positive and we assume usual definitions of profit. Concept / Approach: Let the original cost price be C. The original profit is 220 percent of C, so profit equals 2.20 * C and selling price equals cost plus profit equals 3.20 * C. After the cost increase of 25 percent, the new cost price becomes 1.25 * C, while selling price remains 3.20 * C. The new profit is selling price minus new cost, and the question asks for this new profit as a percentage of the selling price. Therefore, we compute the ratio of the new profit to the selling price and then multiply by 100. Step-by-Step Solution: Let initial cost price be C rupees.Initial profit equals 220 percent of C, so P equals 2.20 * C.Initial selling price S equals C plus P which is C + 2.20 * C equals 3.20 * C.Now cost price increases by 25 percent, so new cost price C1 equals 1.25 * C.Selling price stays S equals 3.20 * C.New profit P1 equals S minus C1 equals 3.20 * C minus 1.25 * C which is 1.95 * C.New profit as a fraction of selling price equals P1 divided by S equals (1.95 * C) / (3.20 * C) which simplifies to 1.95 / 3.20.Compute this ratio: 1.95 / 3.20 equals approximately 0.609375.Convert to percentage by multiplying by 100 to get about 60.94 percent, which is approximately 61 percent. Verification / Alternative check: We can assume a convenient cost price, for example C equals 100 rupees, to verify. Then selling price S equals 3.20 * 100 equals 320 rupees. After the 25 percent increase, new cost becomes 125 rupees. New profit equals 320 minus 125 equals 195 rupees. Profit as a percentage of selling price equals 195 divided by 320 multiplied by 100 which is again about 60.94 percent. This numerical example confirms the earlier algebraic calculation. Why Other Options Are Wrong: Option 75 percent would require a profit of 0.75 times the selling price, which would mean the cost price is much lower than 25 percent above the original. Option 55 percent underestimates the actual ratio. Option 81 percent would represent a profit very close to the selling price, which contradicts the fact that the cost increased by 25 percent. The only option close to the computed value of about 60.94 percent is 61 percent. Common Pitfalls: Some learners mix up profit percentage on cost price with profit percentage on selling price and try to compare the two directly. Others forget that the selling price remains fixed and recalculate it using the new cost. Keeping track of which quantity changes and which remains constant is critical. It is usually easier to assume a simple numeric value for cost price, perform all calculations, and then translate the final ratio into a percentage of the selling price. Final Answer: After the cost increase, the profit is approximately 61 percent of the selling price.

Question 8

A shopkeeper sells two articles at Rs. 1000 each. On the first article he makes a profit of 20 percent, while on the second article he incurs a loss of 20 percent. What is his overall net result as a percentage, and is it a profit or a loss?

Accepted Answer

Introduction / Context: This is a well known profit and loss pattern where equal percentage gain and loss on equal selling prices or equal cost prices may lead to an overall loss. The main goal is to combine a 20 percent profit and a 20 percent loss on two different transactions of equal selling price and see whether the net result is profit or loss, and by what percentage. Given Data / Assumptions: First article selling price is Rs. 1000 with 20 percent profit. Second article selling price is Rs. 1000 with 20 percent loss. Both articles are independent transactions. We must compute the overall percentage profit or loss on the combined cost price. Standard profit and loss definitions apply. Concept / Approach: As profit and loss percentages are always calculated on cost price, we first find the cost price of each article from its selling price and percentage profit or loss. Then we add both cost prices to obtain the total cost, and add both selling prices to obtain total revenue. The net difference tells us the overall profit or loss. Finally, we compute the net percentage with respect to the total cost price. Step-by-Step Solution: For the first article, selling price S1 equals 1000 rupees and profit is 20 percent.Cost price C1 equals S1 divided by 1.20 which is 1000 / 1.20 equals approximately 833.33 rupees.For the second article, selling price S2 equals 1000 rupees and loss is 20 percent.Selling price in this case is 80 percent of cost, so cost price C2 equals 1000 / 0.80 equals 1250 rupees.Total cost price equals C1 plus C2 which is about 833.33 plus 1250 equals 2083.33 rupees.Total selling price equals S1 plus S2 which is 1000 plus 1000 equals 2000 rupees.Net loss equals total cost price minus total selling price which is 2083.33 minus 2000 equals 83.33 rupees approximately.Percentage loss equals 83.33 divided by 2083.33 multiplied by 100, which is exactly 4 percent. Verification / Alternative check: This scenario is a standard result: a 20 percent gain and a 20 percent loss on equal amounts does not cancel out but results in a net loss. Algebraically, if cost price is 100, a 20 percent profit gives selling price 120, while a 20 percent loss gives selling price 80. The total cost would be 100 plus 100 equals 200 and total selling price would be 120 plus 80 equals 200. That example shows no net profit or loss when the cost prices are equal. However, in this question, the selling prices are equal instead. Equal selling prices with equal percentage gain and loss always lead to a net loss, which can be verified by the detailed numerical calculation shown above. Why Other Options Are Wrong: A 2 percent loss or 3 percent loss would require a smaller difference between total cost and total selling price than the one we computed. A 2.5 percent loss lies between these but also does not match the exact ratio of 83.33 to 2083.33. Only a 4 percent loss aligns with the actual numbers derived from the given percentages and selling prices. Common Pitfalls: Many learners erroneously think that a 20 percent profit and a 20 percent loss should cancel out and give no overall change. This is false because the base amounts for profit and loss are different for each article, due to different cost prices. Another pitfall is to average the two percentages directly, giving zero, which once again ignores that percentage calculations are always on cost price, not on selling price. Carefully computing cost prices first avoids such mistakes. Final Answer: The shopkeeper suffers an overall 4 percent loss on the two articles together.

Question 9

A man sells 35 wafers at Rs. 15 each and incurs a loss of Rs. 40.4 on the transaction. If instead he sells the same 35 wafers at Rs. 18 each, what is his profit or loss in rupees, approximately?

Accepted Answer

Introduction / Context: This question uses two different selling prices for the same quantity of wafers. The first selling price leads to a known loss in rupees, which allows us to determine the total cost price. With that cost price, we can then compute whether there is a profit or loss at the second selling price and by how much. The arithmetic involves basic linear equations on totals rather than percentages. Given Data / Assumptions: First scenario: 35 wafers are sold at Rs. 15 each. Loss in the first scenario is Rs. 40.4. Second scenario: the same 35 wafers are sold at Rs. 18 each. The cost price per wafer remains the same in both scenarios. We must find the profit or loss in rupees in the second scenario, approximately. Concept / Approach: First, compute the total selling price in the loss scenario, and then add the loss to obtain the total cost price. From that total cost price, divide by the number of wafers to get the cost price per wafer. Next, compute the total selling price in the second scenario using the higher selling price. Finally, subtract the total cost price from this new selling price to see the net profit or loss. Due to a slightly awkward number 40.4, the final profit will be approximate, so we match the closest integer option. Step-by-Step Solution: Total selling price in the first scenario equals 35 * 15 which is 525 rupees.There is a loss of 40.4 rupees, so total cost price equals 525 plus 40.4 which is 565.4 rupees.Cost price per wafer equals 565.4 divided by 35, approximately 16.16 rupees per wafer.In the second scenario, selling price per wafer is 18 rupees.Total selling price in the second scenario equals 35 * 18 which is 630 rupees.Profit in the second scenario equals total selling price minus total cost price equals 630 minus 565.4 which is 64.6 rupees approximately.Among the given options, the closest integer value to 64.6 is 64 rupees, which we take as the approximate profit. Verification / Alternative check: We can also check roughly by estimating cost per wafer as about 16 rupees. If cost per wafer were exactly 16 rupees, total cost would be 35 * 16 equals 560 rupees. At 15 rupees each, selling price is 525 rupees, giving a loss of 35 rupees, which is a little less than the given 40.4 rupees. At 18 rupees per wafer, selling price is 630 rupees. With total cost near 565 to 570 rupees, the profit should be slightly above 60 rupees, which is consistent with the 64.6 rupee calculation. Thus, an answer around 64 rupees is reasonable and matches the closest option. Why Other Options Are Wrong: Option 52 rupees would imply a much lower difference between the new selling price and the cost price, which contradicts the detailed calculation based on the given loss. Option 72 rupees would require either a lower cost price or higher selling price than we actually have. Option 55 rupees is also not close enough to the derived profit. Only 64 rupees correctly approximates the computed profit of about 64.6 rupees. Common Pitfalls: Some learners mistakenly compute the profit in the second scenario relative to the first selling price instead of the cost price, which is incorrect. Others ignore the decimal in 40.4 and assume a neat cost calculation, leading to small discrepancies. In aptitude tests, such slight differences are often rounded, so it is important to look for the option that is closest to the calculated result, not necessarily an exact match when decimals are involved. Final Answer: When the wafers are sold at Rs. 18 each, the man makes an approximate profit of Rs. 64.

Question 10

A certain sum of money is invested for one year at a certain annual rate of simple interest. If the rate of interest is increased by 3 percentage points, then the interest earned in one year becomes 25 percent more than the interest earned earlier. …

Accepted Answer

Introduction / Context: This question deals with simple interest and the effect of changing the interest rate. The investment period is fixed at one year. We are told that increasing the rate by a fixed number of percentage points increases the interest amount by a certain percentage compared to the original interest. From this relationship, we must determine the original annual interest rate. Given Data / Assumptions: Principal amount is some fixed sum P. Initial annual simple interest rate is r percent. Time period is one year in both cases. New annual rate is r + 3 percent. Interest at the new rate is 25 percent more than interest at the old rate. We must find r, the original rate of interest. Concept / Approach: For simple interest, the interest for one year equals principal multiplied by rate divided by 100, because time is one year. Let the original interest be I1 and the new interest be I2. Then I1 equals P * r / 100 and I2 equals P * (r + 3) / 100. We are told that I2 equals 1.25 times I1. Since P and 100 are common factors, they cancel out when we form the ratio, leaving an equation purely in terms of r. Solving this equation gives the original rate of interest. Step-by-Step Solution: Let principal be P rupees and original rate be r percent per annum.Original interest I1 equals P * r / 100.New rate is r + 3 percent per annum.New interest I2 equals P * (r + 3) / 100.According to the problem, the new interest is 25 percent more than the old interest, so I2 equals 1.25 * I1.Substitute the expressions: P * (r + 3) / 100 equals 1.25 * (P * r / 100).Cancel common factors P and 100 to obtain r + 3 equals 1.25 * r.Rewrite 1.25 * r as r + 0.25 * r.So the equation becomes r + 3 equals r + 0.25 * r, which simplifies to 3 equals 0.25 * r.Thus r equals 3 / 0.25 which is 12 percent per annum. Verification / Alternative check: We can verify by choosing a convenient principal, say P equals 100 rupees. At an original rate of 12 percent, the interest in one year is 12 rupees. If the rate increases by 3 percent, the new rate becomes 15 percent, giving an interest of 15 rupees. The increase in interest is 3 rupees, which is 25 percent of the original interest of 12 rupees, since 3 / 12 * 100 equals 25 percent. This numerical check confirms that 12 percent is indeed the correct original rate. Why Other Options Are Wrong: If the original rate were 4 percent, increasing the rate to 7 percent would make the interest 75 percent more, not 25 percent more. For 6 percent, increasing to 9 percent would produce a 50 percent increase in interest. For 8 percent, moving to 11 percent yields a 37.5 percent increase. Only 12 percent gives an increase from 12 to 15 rupees, which is exactly a 25 percent rise in the interest amount. Common Pitfalls: Some learners mistakenly interpret 3 percent higher as 3 percent of the original rate instead of three percentage points. Others forget that the principal and period remain constant, and they overcomplicate the calculation by including time factors unnecessarily. Writing down the simple interest formula for both cases and then forming the ratio is the easiest way to see that principal and time cancel out, leaving a simple linear equation in r. Final Answer: The original annual simple interest rate was 12 percent per annum.

Question 11

The price of an article has been reduced by 35 percent. By what percentage must the reduced price now be increased in order to restore the article to its original price?

Accepted Answer

Introduction / Context: This question tests understanding of successive percentage changes. A common misconception is that an equal percentage increase will reverse a given percentage decrease, but this is not true because the base values change. Here the price is reduced by 35 percent, and we must find the percentage increase on the reduced price that restores the original price. Given Data / Assumptions: Original price of the article is some amount, say P. The price is reduced by 35 percent. The reduced price needs to be raised back to the original price. We must compute the required percentage increase on the reduced price. All changes are based on simple percentage calculations. Concept / Approach: Let the original price be P. A reduction of 35 percent means the new price equals 65 percent of P, that is 0.65 * P. To restore the price to P, we need to increase the reduced price up to P. The increase amount is P minus 0.65 * P which is 0.35 * P. The required percentage increase is this increase amount divided by the reduced price, multiplied by 100. This ratio is greater than 35 percent because the base for the increase is smaller than the original price. Step-by-Step Solution: Let original price be P rupees.After a 35 percent reduction, the reduced price equals P * (1 minus 0.35) equals 0.65 * P.To restore the original price, we must increase this reduced price back to P.The required increase amount equals P minus 0.65 * P equals 0.35 * P.Required percentage increase equals (increase amount divided by reduced price) multiplied by 100.So percentage increase equals (0.35 * P) / (0.65 * P) * 100.The P cancels, leaving 0.35 / 0.65 * 100.Compute 0.35 / 0.65 equals 35 / 65 which simplifies to 7 / 13, or approximately 0.53846.Thus the required percentage increase is about 0.53846 * 100 equals 53.846 percent, which we write as 53.84 percent. Verification / Alternative check: We can choose a simple value for P, for example 100 rupees, to verify. A 35 percent reduction brings the price down to 65 rupees. To get back from 65 rupees to 100 rupees, the increase required is 35 rupees. As a percentage of 65 rupees, this is 35 / 65 * 100 which again gives 53.846 percent. This numerical example confirms the general algebraic derivation. Why Other Options Are Wrong: Values 51.8 percent, 49.25 percent, and 47.2 percent all correspond to smaller increases that would not raise the reduced price fully back to the original value. Only 53.84 percent is large enough to convert 65 percent of the original price back to 100 percent. Any smaller percentage would leave the price below the original level. Common Pitfalls: A very common error is to say that a 35 percent increase reverses a 35 percent decrease. This is incorrect because the 35 percent decrease is applied on the original price, while the subsequent increase is applied on the reduced price, which is smaller. Another mistake is to compute the difference between 100 and 35 and then use that directly as a percentage without considering the correct base. Always define a variable for the original value and apply percentage changes stepwise to avoid these traps. Final Answer: The reduced price must be increased by 53.84 percent to restore the original price.

Question 12

Mr. Kiran sells a bus for Rs. 18700 and incurs a loss of 15 percent. At what price should he sell the bus in order to earn a profit of 15 percent on its cost price instead?

Accepted Answer

Introduction / Context: This question is a straightforward profit and loss problem where the same asset, a bus, is sold under two different conditions. The first sale incurs a known percentage loss, which allows us to determine the cost price. The second sale is hypothetical and asks for a selling price that would give a specified profit percentage on the same cost price. It uses standard percentage relationships between cost price, selling price, profit, and loss. Given Data / Assumptions: First selling price of the bus is Rs. 18700. At this price there is a loss of 15 percent. The cost price remains the same for both situations. We want to find the selling price that generates a 15 percent profit instead. We use the usual definitions of profit and loss based on cost price. Concept / Approach: When there is a loss of 15 percent, the selling price is 85 percent of the cost price. We can therefore express cost price in terms of the known selling price. Once we know the cost price, we simply compute the selling price corresponding to a 15 percent profit, which is 115 percent of the cost price. This two step procedure is common in questions where the same item is sold at different profit or loss percentages. Step-by-Step Solution: Let cost price of the bus be C rupees.There is a 15 percent loss when the bus is sold for 18700 rupees.A 15 percent loss means selling price equals 85 percent of cost price, so 18700 equals 0.85 * C.Therefore C equals 18700 divided by 0.85.Compute C as 18700 / 0.85 equals 22000 rupees.Now we want a 15 percent profit on this cost price.A 15 percent profit corresponds to a selling price of 115 percent of cost price, so required selling price equals 1.15 * 22000.Compute 1.15 * 22000 equals 25300 rupees. Verification / Alternative check: We can verify by checking percentage changes. At a selling price of 18700 rupees, the loss is 22000 minus 18700 which is 3300 rupees. The loss percentage is 3300 divided by 22000 multiplied by 100 which is 15 percent, as given. At the new selling price of 25300 rupees, the profit is 25300 minus 22000 which is 3300 rupees. This profit is also 3300 divided by 22000 times 100 which equals 15 percent. Thus both the loss and the profit percentages match the problem conditions, confirming that the calculations are correct. Why Other Options Are Wrong: Options 25523, 25522, and 25521 are close numerically but do not correspond to exactly 15 percent profit on a cost price of 22000 rupees. They would give profits slightly more than 3300 rupees and therefore profit percentages slightly above 15 percent. Only 25300 rupees gives a profit of exactly 3300 rupees, which is 15 percent of 22000 rupees. Common Pitfalls: Some learners mistakenly treat 18700 as the cost price and directly increase it by 15 percent to find a new selling price, which is incorrect. The cost price must first be computed using the loss information. Others confuse loss percent and profit percent and attempt to average them or combine percentages directly. Always treat each scenario separately, find the common cost price, and then apply the required percentage for the new selling price. Final Answer: To earn a profit of 15 percent, Mr. Kiran should sell the bus for Rs. 25300.

Question 13

A shopkeeper sells a glass for Rs. 1965 at a loss of 25%. If instead he sells the same glass for Rs. 3013, then what percentage profit will he earn on the cost price?

Accepted Answer

Introduction / Context: This profit and loss question checks whether you can move comfortably between selling price, cost price, loss percentage and profit percentage. A shopkeeper first sells a glass at a loss and then imagines selling the same glass at a higher price. You are asked to compute the profit percentage in the second case, using the same cost price. Questions of this type are extremely common in aptitude exams because they test basic percentage manipulation and the understanding that the cost price remains fixed for a given item. Given Data / Assumptions: - First selling price (with loss) = Rs. 1965. - Loss percentage in the first sale = 25%. - Second selling price (hypothetical) = Rs. 3013. - Cost price of the glass remains the same in both cases. - We need the profit percentage for the second selling price. Concept / Approach: To solve this, we first recover the cost price from the loss information. A loss of 25% means the selling price is 75% of the cost price. Once cost price is known, we can compare it with the second selling price to compute the profit percentage. In percentage terms, loss% or profit% is always calculated with respect to the cost price unless clearly stated otherwise. Therefore, the main steps are: find cost price using loss formula, then find profit percentage using the profit formula. Step-by-Step Solution: Step 1: Let the cost price be CP. A loss of 25% means that the first selling price SP1 = 75% of CP. Step 2: Mathematically, SP1 = (75 / 100) * CP = 0.75 * CP. Step 3: We are given SP1 = 1965. So, 0.75 * CP = 1965. Step 4: Therefore, CP = 1965 / 0.75. Step 5: CP = 2620 rupees. Step 6: Now, the second selling price SP2 is 3013 rupees. Step 7: Profit in the second scenario = SP2 - CP = 3013 - 2620 = 393 rupees. Step 8: Profit percentage = (Profit / CP) * 100. Step 9: Profit percentage = (393 / 2620) * 100. Step 10: This simplifies exactly to 15% profit. Verification / Alternative check: We can verify the calculation quickly. If CP is 2620, then a 25% loss should give SP1 = 2620 - 0.25 * 2620. The loss amount is 655, so SP1 = 2620 - 655 = 1965, which matches the question data. For the second selling price, a 15% profit on 2620 is 2620 * 1.15 = 3013. This exactly matches the given second selling price, confirming that the profit percentage is correctly computed as 15%. Why Other Options Are Wrong: 10.4% profit is too small because the rise from 1965 to 3013 is significant relative to the cost price. 13% profit is also less than the true value and does not reproduce the given selling price when applied to 2620. 20% profit would produce a selling price of 2620 * 1.20 = 3144, which is greater than 3013 and therefore inconsistent with the question. Only 15% profit correctly matches the data. Common Pitfalls: Many learners mistakenly treat the 25% as being on the selling price instead of the cost price. Another common mistake is to directly compare the two selling prices and calculate a percentage difference, which is incorrect because profit and loss percentages must be based on the cost price. It is also easy to mis-handle the division by 0.75, so it is wise to verify the cost price by checking both loss and profit scenarios against the given selling prices. Final Answer: The shopkeeper earns a 15% profit on the cost price when he sells the glass for Rs. 3013 instead of Rs. 1965.

Question 14

The cost price of 60 identical articles is equal to the selling price of x articles. If the trader earns a profit of 20%, what is the value of x?

Accepted Answer

Introduction / Context: This problem tests your understanding of how profit percentage links cost price and selling price when the number of articles changes. Instead of giving the actual prices of the articles, the question provides a relationship between the cost price of a batch and the selling price of a smaller batch. Your task is to use the profit percentage to connect these quantities and solve for the unknown number of articles x. Such questions appear frequently in aptitude and banking exams because they check ratio and proportion skills in the context of profit and loss. Given Data / Assumptions: - Cost price of 60 articles is given in symbolic form. - Selling price of x articles is equal to the cost price of 60 articles. - Profit percentage on each article is 20%. - All articles are identical, so cost price per article is the same. - We need to determine the value of x. Concept / Approach: Let the cost price of one article be C. Then the cost price of 60 articles becomes 60 * C. Profit of 20% means the selling price of one article S is given by S = C * (1 + 20 / 100) = 1.2 * C. The key line in the question states that the total selling price of x articles is numerically equal to the cost price of 60 articles. Therefore, x * S = 60 * C. We substitute S = 1.2 * C and solve for x. The cost price C cancels out, showing that we do not need its actual value. Step-by-Step Solution: Step 1: Let cost price of one article be C. Step 2: Then cost price of 60 articles = 60 * C. Step 3: Profit is 20%, so selling price of one article S = C * 1.20. Step 4: Given that selling price of x articles = cost price of 60 articles. Step 5: Hence, x * S = 60 * C. Step 6: Substitute S = 1.20 * C to get x * 1.20 * C = 60 * C. Step 7: Cancel C from both sides to obtain 1.20 * x = 60. Step 8: Therefore, x = 60 / 1.20 = 50. Verification / Alternative check: Assume a simple cost price to verify. Let C = Rs. 10. Then cost price of 60 articles is 600. Selling price of one article with 20% profit is 12. If x = 50, then selling price of 50 articles is 50 * 12 = 600, which matches the cost price of 60 articles. Hence, x = 50 is consistent. Any other value of x will not match the equality between total selling price and total cost price. Why Other Options Are Wrong: If x = 15 or x = 30, the total selling price would be much smaller than the cost price of 60 articles. If x = 80, the total selling price would exceed the cost price by a large margin and would not satisfy the relationship in the question. Only x = 50 fits both the percentage condition and the equality between cost price and selling price. Common Pitfalls: A common mistake is to assume some arbitrary cost price and selling price and then forget to apply the correct profit percentage. Another error is to treat 20% as a fraction of the selling price instead of the cost price. Some students also try to plug numbers directly into an equation without clearly defining the variables, which can lead to confusion. Always define cost price per article, convert the profit percentage correctly, and then use the given relationship between the totals. Final Answer: The number of articles whose selling price equals the cost price of 60 articles at 20% profit is 50.

Question 15

Mohit buys an old bicycle for Rs. 2700 and spends Rs. 500 on its repairs. If he sells the bicycle for Rs. 3520, what is his profit percentage on the total cost?

Accepted Answer

Introduction / Context: This question checks whether you correctly include all cost components when computing profit percentage. Mohit buys a second-hand bicycle and spends additional money on repairs. The true cost price is the sum of the purchase price and the repair expenses. Ignoring the repair cost is a very common mistake in such problems. Once you form the correct total cost, the question is a straightforward profit percentage calculation. Given Data / Assumptions: - Purchase price of the old bicycle = Rs. 2700. - Repair cost incurred by Mohit = Rs. 500. - Selling price of the bicycle after repairs = Rs. 3520. - There are no other hidden costs or taxes. - We are asked to find the profit percentage on the total cost. Concept / Approach: The central concept is that cost price should include all expenditure made to get the asset into saleable condition. Thus, cost price CP = purchase price + repair cost. Profit is defined as Profit = Selling Price - Cost Price. After obtaining the absolute profit, we calculate profit percentage using Profit Percentage = (Profit / Cost Price) * 100. These formulas are standard in profit and loss problems and must be applied systematically. Step-by-Step Solution: Step 1: Compute total cost price CP. Step 2: CP = 2700 + 500 = Rs. 3200. Step 3: Given selling price SP = Rs. 3520. Step 4: Profit = SP - CP = 3520 - 3200 = Rs. 320. Step 5: Profit percentage = (Profit / CP) * 100. Step 6: Profit percentage = (320 / 3200) * 100. Step 7: Simplify: 320 / 3200 = 0.10, so profit percentage = 10%. Verification / Alternative check: We can also check by scaling. If the cost price is 3200, then 10% of 3200 is 320. Adding this to the cost gives a selling price of 3520, which exactly matches the given selling price. Therefore the profit percentage must be 10%. If we had mistakenly used only 2700 as cost, the profit would seem to be 820, leading to a much higher and incorrect percentage, which shows why including repair cost is essential. Why Other Options Are Wrong: A profit of 12.5%, 15%, or 20% on a cost of 3200 would lead to profits of 400, 480, or 640 respectively, resulting in selling prices of 3600, 3680, or 3840. None of these match the actual selling price of 3520. These incorrect options often trap students who forget the repair cost or miscalculate the percentage. Only 10% keeps the cost and selling price relationship consistent. Common Pitfalls: The biggest pitfall is forgetting to add the repair cost to the initial purchase price. Students sometimes treat repair cost as something separate and compute profit only on the original purchase price, which is not correct from a business perspective. Another mistake is computing percentage on the selling price instead of the cost price. Always remember: unless clearly stated otherwise, profit and loss percentages are based on cost price. Final Answer: Mohit makes a 10% profit on the bicycle when he sells it for Rs. 3520 after spending on repairs.

Question 16

A shopkeeper marks up his goods by 80% above cost price and then offers a discount of 20% on the marked price. If the cost price of the article is Rs. 450, what is the final selling price?

Accepted Answer

Introduction / Context: This question combines both markup and discount in a single transaction, which is very common in real life. A shopkeeper increases the price of an item above its cost price (markup) and later offers a discount to attract buyers. The effective selling price depends on both of these percentage changes. Aptitude exams often test whether you know that markup and discount are applied one after the other on different bases, not simply added or subtracted as raw percentages. Given Data / Assumptions: - Cost price of the article = Rs. 450. - Markup percentage above cost price = 80%. - Discount percentage on marked price = 20%. - We need the final selling price after both operations. - There are no extra taxes or hidden charges. Concept / Approach: First compute the marked price using Marked Price = Cost Price * (1 + Markup Percentage / 100). Then apply the discount to the marked price using Selling Price = Marked Price * (1 - Discount Percentage / 100). It is crucial to note that markup is calculated on the cost price, while discount is calculated on the marked price. You cannot simply subtract 20% from 80% to say the net percentage is 60%, because the bases are different in each step. Step-by-Step Solution: Step 1: Compute the marked price (MP). Step 2: MP = 450 * (1 + 80 / 100) = 450 * 1.80. Step 3: MP = 810 rupees. Step 4: Apply 20% discount on the marked price to get selling price (SP). Step 5: SP = MP * (1 - 20 / 100) = 810 * 0.80. Step 6: SP = 648 rupees. Step 7: So the article finally sells for Rs. 648. Verification / Alternative check: To verify logically, calculate the effective factor of these two successive changes. Markup factor is 1.80 and discount factor is 0.80. The combined factor is 1.80 * 0.80 = 1.44. This factor acts directly on the cost price. Thus effective selling price = 450 * 1.44 = 648, which matches our earlier result. Therefore both the stepwise and combined-factor methods give the same answer, confirming that the calculations are reliable. Why Other Options Are Wrong: Rs. 548, Rs. 748, and Rs. 848 correspond to incorrect combinations of percentages or to mistakes such as subtracting discount from markup directly, or applying discount on cost price instead of marked price. For example, if someone incorrectly applied discount on cost price, they might compute 450 * 0.80 = 360 and then attempt to reapply markup, which is wrong. Only Rs. 648 respects the correct order and bases of these percentage operations. Common Pitfalls: Many students incorrectly think that an 80% markup and 20% discount give a net 60% increase, but this is not accurate because the discount is applied on the higher marked price, not on the cost price. Another pitfall is using the wrong base for percentage calculations or mixing up cost price, marked price and selling price. Always process the steps in order: first markup on cost price, then discount on marked price. Final Answer: The final selling price of the article after an 80% markup and 20% discount on a cost price of Rs. 450 is Rs. 648.

Question 17

The marked price of a chair is 40% more than its cost price. After allowing a discount of Rs. 40, the chair is sold for Rs. 520. What is the profit percentage earned on the chair?

Accepted Answer

Introduction / Context: This question combines markup (in percentage form) and a fixed discount amount to test your understanding of how to move back to the cost price and then compute profit percentage. The marked price is given as a percentage above cost price, while the actual selling price is the marked price minus a fixed rupee discount. From this information you must recover the cost price and then calculate the profit percentage achieved on the sale of the chair. Given Data / Assumptions: - The marked price of the chair is 40% above its cost price. - The discount offered on the marked price is Rs. 40. - The final selling price after discount is Rs. 520. - There are no additional costs or taxes. - We must find the profit percentage on the cost price. Concept / Approach: Let the cost price be CP. Then marked price MP = CP * (1 + 40 / 100) = 1.4 * CP. The selling price is given as MP - 40 and is known to be Rs. 520. So we can set up the equation 1.4 * CP - 40 = 520 and solve for CP. Once CP is known, profit is Selling Price - Cost Price, and profit percentage is (Profit / CP) * 100. This structured approach ensures every step is logically consistent and avoids guesswork. Step-by-Step Solution: Step 1: Let cost price of the chair be CP. Step 2: Marked price MP = 1.4 * CP. Step 3: After discount of Rs. 40, selling price SP = MP - 40. Step 4: Given SP = 520, so 1.4 * CP - 40 = 520. Step 5: Add 40 to both sides: 1.4 * CP = 560. Step 6: CP = 560 / 1.4 = 400 rupees. Step 7: Profit = SP - CP = 520 - 400 = 120 rupees. Step 8: Profit percentage = (120 / 400) * 100 = 30%. Verification / Alternative check: We can verify by reconstructing the marked price. If CP = 400, then MP = 400 * 1.4 = 560. Discount is Rs. 40, so SP = 560 - 40 = 520, which matches the question. The profit is 520 - 400 = 120, and 120 is exactly 30% of 400. Therefore, the computed profit percentage of 30% is fully consistent with all given figures. Why Other Options Are Wrong: A 25% profit would give a profit of only 100 on a cost of 400, leading to a selling price of 500, not 520. A 33% profit would produce an approximate selling price of 532, and a 40% profit would result in a selling price of 560, equal to the marked price without discount. None of these match the provided selling price and discount data. Only 30% satisfies the conditions exactly. Common Pitfalls: Some students wrongly treat the discount as 40% instead of Rs. 40 because they are used to percent-based discounts. Others forget that profit is computed on cost price, not on marked price. A further mistake is to assume that 40% markup and Rs. 40 discount can be combined directly without setting up an equation. Defining CP, writing expressions for MP and SP, and then solving carefully is the safest route. Final Answer: The profit earned on the sale of the chair is 30% of its cost price.

Question 18

A shopkeeper sells 5 identical items and earns a profit equal to the selling price of 1 item. What is his profit percentage on the cost price?

Accepted Answer

Introduction / Context: This problem uses a simple relationship between total profit and selling price to test your algebraic thinking. The shopkeeper sells 5 items and is told that the total profit he earns is equal to the selling price of one item. By translating this statement into an equation, you can determine the profit percentage on the cost price. Questions of this kind are common in competitive exams because they combine basic profit concepts with a short algebraic step. Given Data / Assumptions: - The shopkeeper sells 5 identical items. - Total profit on the sale of these 5 items equals the selling price of 1 item. - All items have the same cost price and selling price. - We need the profit percentage on the cost price. - No additional costs or discounts are involved. Concept / Approach: Let cost price of each item be C and selling price of each item be S. Then, for 5 items, total cost is 5 * C and total selling price is 5 * S. Profit = Total Selling Price - Total Cost Price = 5S - 5C. The question states that this profit is equal to the selling price of 1 item, i.e., 5S - 5C = S. We solve this equation to find the ratio S / C, and then use that ratio to compute the profit percentage as ((S - C) / C) * 100. Step-by-Step Solution: Step 1: Let cost price per item be C and selling price per item be S. Step 2: Total cost for 5 items = 5 * C. Step 3: Total selling price for 5 items = 5 * S. Step 4: Profit = Total selling price - Total cost price = 5S - 5C. Step 5: Given that profit = selling price of 1 item = S. Step 6: So, 5S - 5C = S. Step 7: Rearrange: 5S - S = 5C, so 4S = 5C. Step 8: Therefore, S = (5 / 4) * C. Step 9: Profit per item = S - C = (5 / 4) * C - C = (1 / 4) * C. Step 10: Profit percentage = (Profit per item / C) * 100 = (C / 4) / C * 100 = 25%. Verification / Alternative check: Assume a convenient cost price, say C = Rs. 4. Then S = (5 / 4) * 4 = Rs. 5. For 5 items, total cost = 5 * 4 = Rs. 20 and total selling price = 5 * 5 = Rs. 25. Profit = 25 - 20 = Rs. 5, which is exactly equal to the selling price of 1 item. Profit percentage = (1 / 4) * 100 = 25%. This numerical example confirms the algebraic result. Why Other Options Are Wrong: A 20% profit would correspond to S = 1.2 * C and would not satisfy the equation 5S - 5C = S. Similarly, profit percentages of 16% or 22.5% give different S to C ratios, none of which make the total profit equal to S for 5 items. Only 25% profit gives a neat and exact equality as described in the problem statement. Common Pitfalls: Students sometimes misinterpret the statement and think that profit on each item equals selling price of one item, which is incorrect. The profit equality mentioned in the problem is about total profit on 5 items. Another mistake is not creating an algebraic equation and instead trying to guess the percentage. Systematically defining variables and writing the relationship avoids these errors. Final Answer: The shopkeeper earns a 25% profit on the cost price of each item.

Question 19

A trader buys 500 kg of cotton for Rs. 9000. Due to rain, 10% of the cotton is spoiled and cannot be sold. At what selling price per kilogram should he sell the remaining cotton to earn a profit of 10% on his total investment?

Accepted Answer

Introduction / Context: This question tests your ability to handle loss of quantity and desired profit simultaneously. The trader buys a bulk quantity of cotton, but a portion becomes unsaleable because it is spoiled by rain. He now needs to adjust the selling price of the remaining good cotton so that, despite the loss of quantity, he still earns a 10% profit on his total cost. This is a realistic business scenario and a classic concept in profit and loss involving wastage. Given Data / Assumptions: - Total quantity purchased = 500 kg of cotton. - Total cost price = Rs. 9000. - Percentage of cotton spoiled = 10%. - Spoiled cotton cannot be sold, so only the remaining 90% is saleable. - Desired overall profit on total cost = 10%. - We need the selling price per kg for the remaining cotton. Concept / Approach: First, calculate how many kilograms remain after 10% is spoiled. Then, compute the total revenue required to earn a 10% profit on the total cost price of Rs. 9000. Once you know the target revenue and the saleable quantity, the required selling price per kilogram is simply Target Revenue divided by Saleable Quantity. This method ensures that the loss from spoiled cotton is recovered in the price of the remaining cotton while still maintaining the desired profit percentage on the original investment. Step-by-Step Solution: Step 1: Find the quantity spoiled. Step 2: 10% of 500 kg = (10 / 100) * 500 = 50 kg. Step 3: Saleable quantity = 500 kg - 50 kg = 450 kg. Step 4: Total cost price (CP) = Rs. 9000. Step 5: Desired profit = 10% of CP = (10 / 100) * 9000 = Rs. 900. Step 6: Required total revenue (selling price of saleable cotton) = CP + Profit = 9000 + 900 = Rs. 9900. Step 7: Let required selling price per kg be SP. Step 8: Total revenue = SP * 450 = 9900. Step 9: Therefore SP = 9900 / 450 = Rs. 22 per kg. Verification / Alternative check: We can cross-check by recomputing the effective situation. If the trader sells 450 kg at Rs. 22 per kg, his revenue is 450 * 22 = Rs. 9900. His initial cost was Rs. 9000, so profit = 9900 - 9000 = Rs. 900. Profit percentage = (900 / 9000) * 100 = 10%. Thus all conditions of the question are satisfied exactly. The spoiled 50 kg are effectively absorbed in the higher price of the remaining 450 kg. Why Other Options Are Wrong: At Rs. 20 per kg or Rs. 25 per kg, the total revenue would be 450 * 20 = 9000 (no profit) or 450 * 25 = 11250 (much more than 10% profit). At Rs. 30 per kg, the profit would be even higher. Only Rs. 22 per kg gives exactly a 10% profit while accounting for the loss of 10% of the quantity. Therefore, all other options are inconsistent with the required profit percentage. Common Pitfalls: A common mistake is to calculate selling price per kg simply by adding 10% to the average cost per kg, without adjusting for the loss in quantity. The effective cost per kg of saleable cotton is higher than the original because some quantity has been lost. Another pitfall is to take 10% of 500 as extra profit instead of understanding that it represents wastage. Always adjust the saleable quantity first, then compute the required revenue for the target profit, and finally derive the selling price per kg. Final Answer: The trader should sell the remaining cotton at Rs. 22 per kg to earn a 10% profit on his total investment.

Question 20

A shopkeeper wants to earn 33% profit on an article even after offering a 30% discount to customers. By what percentage above the cost price should he mark the article?

Accepted Answer

Introduction / Context: In this question, a shopkeeper plans pricing in such a way that, even after giving a substantial discount, he still earns a desired profit on the cost price. This is a classic combination of markup and discount where you must work backward to find the required marked price. The core idea is that the final selling price after discount must correspond to the desired profit percentage on the cost price, and the marked price is adjusted accordingly. Given Data / Assumptions: - Desired profit percentage on cost price = 33%. - Discount percentage offered to customers = 30% on marked price. - The article has a definite cost price, denoted by CP. - We must find by what percentage above CP the article should be marked. - There are no extra taxes, and discount is applied only once. Concept / Approach: Let the cost price be CP. To achieve 33% profit, the required selling price after discount must be SP = 1.33 * CP. The shopkeeper will mark the price at some level MP such that, after giving a 30% discount, the customer pays exactly SP. A discount of 30% means the customer pays 70% of the marked price, so SP = 0.70 * MP. Combine these ideas: 0.70 * MP = 1.33 * CP. Solve this equation to express MP as a multiple of CP, then convert that multiple into a markup percentage above cost price. Step-by-Step Solution: Step 1: Let cost price be CP. Step 2: Desired profit = 33% of CP, so selling price after discount SP = CP * 1.33. Step 3: Let marked price be MP. Step 4: Discount is 30%, so the buyer actually pays 70% of MP. Step 5: Hence SP = 0.70 * MP. Step 6: Equate the expressions for SP: 0.70 * MP = 1.33 * CP. Step 7: MP = (1.33 / 0.70) * CP. Step 8: Compute the factor: 1.33 / 0.70 = 1.9. Step 9: Therefore MP = 1.9 * CP. Step 10: This means the marked price is 90% above the cost price, because 1.9 * CP = CP + 0.9 * CP. Verification / Alternative check: Assume CP = Rs. 100 for a quick check. To earn 33% profit, SP must be Rs. 133. If the shopkeeper marks at 90% above CP, MP = 100 * 1.9 = Rs. 190. Discount of 30% on 190 is 0.30 * 190 = 57, so the buyer pays 190 - 57 = Rs. 133. This matches the required selling price for 33% profit, confirming that a 90% markup is correct. Why Other Options Are Wrong: If the markup were only 63%, 69%, or 72%, the effective selling price after 30% discount would be less than 1.33 times the cost price, resulting in a lower profit percentage. Each smaller markup produces a smaller final selling price and thus fails to achieve the target 33% profit. Only a 90% markup creates a situation where a 30% discount still leaves the shopkeeper with the desired gain. Common Pitfalls: A frequent error is to subtract the discount percentage directly from the desired profit percentage, for example 33% + 30% or 33% - 30%, which is not logically correct. Another mistake is to apply discount on the cost price instead of the marked price. Always remember that discount is applied on the marked price and profit is calculated on the cost price. Setting up proper equations connecting marked price, selling price, and cost price is the safest and most systematic method. Final Answer: The shopkeeper should mark the article at 90% above the cost price to earn 33% profit after giving a 30% discount.

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