Question 1

If the cost price of an article is 25% of its selling price, what is the profit percentage made on the article?

Accepted Answer

Introduction / Context: This problem checks understanding of the relationship between cost price, selling price and profit percentage when the cost price is given as a percentage of the selling price. Instead of the usual situation where selling price is expressed as a percentage above cost, here the direction is reversed, which can confuse learners who do not carefully interpret the statement. Given Data / Assumptions: Cost price (CP) is 25% of selling price (SP). All transactions involve a single article. We must find profit percentage based on cost price. Concept / Approach: If CP is 25% of SP, then CP = 0.25 * SP, or equivalently SP = 4 * CP. Profit is defined as SP - CP, and profit percentage is (Profit / CP) * 100. Once we express SP in terms of CP, we can find the ratio SP / CP and therefore the profit percentage. Working in terms of a symbolic cost price CP keeps the steps simple. Step-by-Step Solution: Step 1: Let cost price be CP and selling price be SP.Step 2: Given that CP is 25% of SP, so CP = 0.25 * SP.Step 3: Rearranging, SP = CP / 0.25 = 4 * CP.Step 4: Profit = SP - CP = 4CP - CP = 3CP.Step 5: Profit percentage = (Profit / CP) * 100 = (3CP / CP) * 100 = 300%. Verification / Alternative check: Assume CP = Rs. 100 for convenience.Then CP = 25% of SP implies 100 = 0.25 * SP, giving SP = 400 rupees.Profit = 400 - 100 = 300 rupees, and profit percentage = 300 / 100 * 100 = 300%, confirming the formula-based solution. Why Other Options Are Wrong: Profit percentages such as 150%, 200% or 250% would correspond to SP values of 2.5CP, 3CP or 3.5CP respectively, none of which matches the exact relationship CP = 0.25 * SP. A profit of 350% would be even larger and not consistent with SP = 4CP. Only 300% is aligned with SP being four times CP. Common Pitfalls: Many learners mistakenly interpret “cost price is 25% of selling price” as “selling price is 25% above cost price,” which would be a much smaller increase. Others incorrectly use (SP / CP) * 100 as profit percentage and forget to subtract one before converting to a percentage. Being careful about which quantity is a percentage of which prevents these misreadings. Final Answer: The profit percentage made on the article is 300%.

Question 2

A trader sells an article at a loss of 5%. When he increases the selling price by Rs. 65, he instead gains 3.33% (that is, one-thirtieth of the cost price). If he sells the same article at Rs. 936, what is his profit percentage?

Accepted Answer

Introduction / Context: This question links two different selling prices with two different profit or loss percentages to determine the cost price of an article. Once the cost price is known, a third selling price is used to compute the profit percentage. The problem tests algebraic setup and understanding that small changes in selling price can shift a transaction from loss to profit. Given Data / Assumptions: At the first selling price, there is a loss of 5%. When the selling price is increased by Rs. 65, there is a gain of 3.33% (approximately one-thirtieth of cost). The same article is then sold at Rs. 936. We must find the profit percentage when the selling price is Rs. 936. Concept / Approach: Let the cost price be C. A loss of 5% means the first selling price S1 = 0.95C. A profit of 3.33% (which is 1 / 30 of C) means the second selling price S2 = C * (1 + 1 / 30) = 31C / 30. We know S2 = S1 + 65. Solving this equation gives C. Finally, profit at selling price Rs. 936 is (936 - C), so profit percentage is (936 - C) / C * 100. Step-by-Step Solution: Step 1: Let cost price be C rupees.Step 2: First selling price with 5% loss: S1 = 0.95C.Step 3: Second selling price with 3.33% gain: S2 = C * (1 + 1 / 30) = 31C / 30.Step 4: Given that S2 = S1 + 65, so 31C / 30 = 0.95C + 65.Step 5: Convert 0.95C to a fraction: 0.95C = 19C / 20, so 31C / 30 = 19C / 20 + 65.Step 6: Bring terms involving C together: 31C / 30 - 19C / 20 = 65.Step 7: Compute left side with common denominator 60: (62C - 57C) / 60 = 5C / 60 = C / 12 = 65, so C = 780.Step 8: When sold at Rs. 936, profit = 936 - 780 = 156.Step 9: Profit percentage = 156 / 780 * 100 = 0.2 * 100 = 20%. Verification / Alternative check: First selling price at 5% loss: S1 = 0.95 * 780 = 741 rupees.Second selling price should be S1 + 65 = 741 + 65 = 806 rupees.Check 3.33% gain: 806 - 780 = 26, and 26 / 780 * 100 ≈ 3.33%, confirming C = 780 is correct.Then at Rs. 936, profit percentage is indeed 156 / 780 * 100 = 20%. Why Other Options Are Wrong: Profit rates like 15%, 16.67%, or 12.5% correspond to smaller profits at Rs. 936 than the calculated 156 rupees. The option “Data insufficient” is incorrect because the two conditions involving a Rs. 65 change and two percentages uniquely determine the cost price. Only 20% matches the computed value exactly. Common Pitfalls: Some learners approximate 3.33% as 3% or 3.5%, which leads to slightly wrong equations and cost prices. Others forget to convert decimals like 0.95 into exact fractions, causing algebraic mistakes. Being precise about 3.33% as 1 / 30 of the cost price and carefully handling the equation ensure the correct result. Final Answer: When the article is sold for Rs. 936, the trader's profit percentage is 20%.

Question 3

A man bought an article and sold it at a gain of 5%. If he had bought it at 5% less than the original cost price and sold it for Re. 1 less than the original selling price, he would have made a profit of 10%. What was the original cost price of the …

Accepted Answer

Introduction / Context: This is a classic reverse-calculation problem in profit and loss. Two hypothetical scenarios are given, each with different buying and selling conditions and different profit percentages. The question asks for the original cost price. It tests the ability to set up and solve equations using percentage gain and small absolute changes in buying and selling prices. Given Data / Assumptions: Original cost price = C (unknown). Original selling price gives a profit of 5%. In an alternate scenario, cost price is reduced by 5% and selling price is reduced by Re. 1. In the alternate scenario, the profit is 10% on the reduced cost price. We must find C, the original cost price. Concept / Approach: Let the original cost price be C. Then original selling price S1 = 1.05C. In the second scenario, the new cost price is 0.95C and the new selling price is S1 - 1. The problem states that this new selling price corresponds to a 10% gain on 0.95C, so it must equal 1.10 * 0.95C. Equating S1 - 1 with 1.10 * 0.95C gives an equation involving C that can be solved directly. Step-by-Step Solution: Step 1: Let original cost price be C. Original selling price S1 = 1.05C.Step 2: In the alternate scenario, new cost price = 0.95C.Step 3: New selling price is S1 - 1 = 1.05C - 1.Step 4: Profit in the alternate scenario is 10%, so new selling price = 1.10 * 0.95C = 1.045C.Step 5: Equate the two expressions: 1.05C - 1 = 1.045C.Step 6: Rearrange: 1.05C - 1.045C = 1, so 0.005C = 1.Step 7: Therefore C = 1 / 0.005 = 200 rupees. Verification / Alternative check: With C = Rs. 200, original selling price S1 = 1.05 * 200 = Rs. 210, which is a 5% gain.Alternate cost price = 0.95 * 200 = Rs. 190.Alternate selling price = 210 - 1 = Rs. 209.Profit in alternate scenario = 209 - 190 = Rs. 19, and profit percentage = 19 / 190 * 100 = 10%, matching the condition. Why Other Options Are Wrong: For C = Rs. 100, Rs. 150, Rs. 250 or Rs. 300, the alternate selling price obtained by subtracting Re. 1 from the original selling price does not correspond to a 10% profit on the reduced cost price. Only C = Rs. 200 satisfies both the 5% profit in the first case and the 10% profit in the second case. Common Pitfalls: Some learners misapply the 5% reduction by subtracting Rs. 5 instead of 5% of C. Others forget that the second profit percentage is on the reduced cost price, not on the original. A further source of error is failing to align the two selling price expressions correctly when forming the equation. Writing each scenario separately and then equating is essential. Final Answer: The original cost price of the article was Rs. 200.

Question 4

A person incurs a loss of 5% by selling a watch for Rs. 1140. At what price should the watch be sold to earn a profit of 5% on the cost price?

Accepted Answer

Introduction / Context: This question moves from a loss situation to a desired profit on the same item. It requires first recovering the cost price from a given selling price and loss percentage, and then computing a new selling price that yields a specified profit percentage. This type is frequent in basic profit and loss practice. Given Data / Assumptions: The watch is sold at Rs. 1140 with a loss of 5%. The cost price remains the same for both transactions. We want a 5% profit on the cost price in the new sale. We must find the required selling price for 5% profit. Concept / Approach: A loss of 5% means the selling price is 95% of the cost price. From SP = 1140 we can compute CP as 1140 divided by 0.95. Once CP is known, a profit of 5% implies a new selling price equal to 105% of CP. Working systematically with percentages as decimals makes the computation straightforward. Step-by-Step Solution: Step 1: Let CP be the cost price of the watch.Step 2: Loss of 5% implies selling price SP1 = 0.95 * CP.Step 3: Given SP1 = Rs. 1140, so 0.95 * CP = 1140.Step 4: Therefore CP = 1140 / 0.95.Step 5: Calculate CP: 0.95 = 95 / 100, so CP = 1140 * 100 / 95 = 114000 / 95 = Rs. 1200.Step 6: To earn a 5% profit, required selling price SP2 = 1.05 * CP = 1.05 * 1200 = Rs. 1260. Verification / Alternative check: Check the loss case: selling at Rs. 1140 when CP = Rs. 1200 gives loss = 60, and loss percentage = 60 / 1200 * 100 = 5%.Check the profit case: selling at Rs. 1260 gives profit = 1260 - 1200 = 60, and profit percentage = 60 / 1200 * 100 = 5%.Thus both conditions are satisfied with CP = 1200 and SP2 = 1260. Why Other Options Are Wrong: Rs. 1200 corresponds to selling at cost price, giving zero profit. Rs. 1230 would be a profit of 30 on a cost of 1200, which is only 2.5%. Rs. 1290 gives a profit of 90, or 7.5%, and Rs. 1320 gives a profit of 120, or 10%. Only Rs. 1260 yields exactly a 5% profit. Common Pitfalls: Some learners mistakenly subtract 5 rupees instead of 5% or mix up the direction of the percentage, treating 1140 as 105% of cost instead of 95%. Others attempt to find the difference between loss and profit percentages directly without recovering the cost price. Always anchor all calculations on the cost price when dealing with profit and loss percentages. Final Answer: The watch should be sold for Rs. 1260 to earn a 5% profit.

Question 5

What profit percentage is made by selling an article at a certain price, if selling the same article at two-thirds of that price would result in a loss of 20%?

Accepted Answer

Introduction / Context: This question relates two selling prices for the same article: one at which there is a loss and another at which there is a profit. The condition involves a multiplicative relation between the two selling prices. The problem tests algebraic reasoning around the cost price and the connection between loss and profit at different selling levels. Given Data / Assumptions: At two-thirds of some reference selling price S, there is a loss of 20%. The cost price remains the same in all cases. At the full selling price S, there is a profit that we must find as a percentage. The article and all prices are assumed to be consistent for a single transaction. Concept / Approach: Let the higher selling price be S. Then the lower selling price where there is a loss is (2 / 3) * S. A loss of 20% at this lower price means that (2 / 3) * S equals 80% of the cost price. From this, we can express the cost price in terms of S. Once the cost price is known symbolically, the profit at selling price S is S minus cost price, and profit percentage is this profit divided by cost price times 100. Step-by-Step Solution: Step 1: Let higher selling price = S. Lower selling price = (2 / 3)S.Step 2: At lower selling price, there is a loss of 20%, so (2 / 3)S = 0.8 * CP, where CP is cost price.Step 3: Therefore CP = (2S / 3) / 0.8 = (2S / 3) / (4 / 5) = (2S / 3) * (5 / 4) = 10S / 12 = 5S / 6.Step 4: At price S, profit = S - CP = S - 5S / 6 = S / 6.Step 5: Profit percentage = (Profit / CP) * 100 = (S / 6) / (5S / 6) * 100 = (S / 6) * (6 / 5S) * 100 = (1 / 5) * 100 = 20%. Verification / Alternative check: Assume CP = Rs. 100 for an intuitive check.A loss of 20% means lower selling price = 80% of CP = Rs. 80.This lower price corresponds to two-thirds of the higher price, so higher selling price S = 80 * 3 / 2 = Rs. 120.Profit at S: 120 - 100 = Rs. 20, so profit percentage = 20 / 100 * 100 = 20%. Why Other Options Are Wrong: Profit percentages like 15%, 25%, 30% or 35% would correspond to different relationships between CP and S that do not match the given condition that two-thirds of S yields a 20% loss. Only 20% is consistent with the algebraic and numerical checks. Common Pitfalls: One common mistake is to treat the 20% as a profit instead of a loss when setting up the cost price equation. Another is to assume that the difference between 20% loss and some unknown profit can be added directly without considering the multiplicative relationship between prices. Carefully associating each percentage with its correct base (CP or SP) is essential. Final Answer: The profit made by selling at the higher price is 20%.

Question 6

A manufacturer gains 10%, a wholesale dealer gains 15% over the manufacturer's price, and a retailer gains 25% over the wholesale price. If the final retail price of a table is Rs. 1265, what was the original cost of production for the manufacturer?

Accepted Answer

Introduction / Context: This question involves three successive profit margins: manufacturer to wholesaler, wholesaler to retailer, and retailer to customer. It is a practical scenario showing how cumulative markups affect the final selling price. The task is to work backwards from the retail price to find the original cost of production. Given Data / Assumptions: Manufacturer's gain = 10% over his cost of production. Wholesale dealer's gain = 15% over the price paid to the manufacturer. Retailer's gain = 25% over the wholesale price. Final retail price to the customer = Rs. 1265. We must find the manufacturer's cost of production. Concept / Approach: Let the manufacturer's cost be M. The manufacturer sells at 1.10M to the wholesaler. The wholesaler applies a 15% margin, so he sells at 1.15 * 1.10M to the retailer. The retailer then adds 25% and sells at 1.25 times that wholesale price. The product of these three markup factors equals the ratio between the retail price and the manufacturer's cost. We equate this compounded price to Rs. 1265 and solve for M. Step-by-Step Solution: Step 1: Let manufacturer's cost price be M rupees.Step 2: Manufacturer sells to wholesaler at 1.10M.Step 3: Wholesaler sells to retailer at 1.15 * 1.10M = 1.265M.Step 4: Retailer sells to customer at 1.25 * 1.265M = 1.58125M.Step 5: Final retail price is given as Rs. 1265, so 1.58125M = 1265.Step 6: Therefore M = 1265 / 1.58125.Step 7: Note that 1.58125 * 800 = 1265 exactly, so M = Rs. 800. Verification / Alternative check: Manufacturer's cost = Rs. 800. Manufacturer sells at 10% profit: 1.10 * 800 = Rs. 880.Wholesaler sells at 15% profit: 1.15 * 880 = Rs. 1012.Retailer sells at 25% profit: 1.25 * 1012 = Rs. 1265.The chain of markups reproduces the given final price, confirming M = 800. Why Other Options Are Wrong: If M were Rs. 750, 850, 900 or 700, the final retail price after applying 10%, 15% and 25% successively would differ from Rs. 1265. Only with M = Rs. 800 does the compounded markup exactly match the given retail price. Common Pitfalls: Some learners add the percentages directly (10% + 15% + 25%) and attempt to treat the combined markup as a single percentage, which is incorrect because each percentage is applied on a different base. Others may work backwards incorrectly by subtracting 25%, 15% and 10% sequentially without using the proper division by the corresponding factors. Using multiplication and division by accurate decimal factors is the correct approach. Final Answer: The manufacturer's original cost of production for the table was Rs. 800.

Question 7

A car mechanic purchased four old cars for Rs. 1 lakh in total and spent another Rs. 2 lakh on maintenance and repairs of these four cars. He has already sold one of the cars for Rs. 1.2 lakh. At what average selling price should he sell each of the…

Accepted Answer

Introduction / Context: This question is a mixture of total cost accounting and average selling price. The mechanic invests in four cars and additional repairs, sells one car, and wants a target overall profit percentage. We are asked to find the average selling price required for the remaining cars so that the total profit objective is achieved. It is a typical example of combining total cost, partial sales, and average revenue. Given Data / Assumptions: Purchase cost of four old cars = Rs. 1 lakh. Repairs and maintenance for all four cars = Rs. 2 lakh. Total investment = Rs. 3 lakh. One car is already sold for Rs. 1.2 lakh. Mechanic wants an overall profit of 50% on the total investment. We must find the average selling price of each of the three remaining cars. Concept / Approach: A 50% profit on the total cost means that the total revenue from selling all four cars must be 1.5 times the total investment. From this target total revenue, we subtract the amount already received from the first car. The remainder must come from the three remaining cars. Dividing that remainder by 3 gives the required average selling price per car. Step-by-Step Solution: Step 1: Total purchase cost of cars = Rs. 1 lakh, repairs = Rs. 2 lakh.Step 2: Total investment = 1 + 2 = Rs. 3 lakh.Step 3: Required total revenue for 50% profit = 1.5 * 3 lakh = Rs. 4.5 lakh.Step 4: Revenue already received from one car = Rs. 1.2 lakh.Step 5: Revenue still needed from remaining three cars = 4.5 lakh - 1.2 lakh = Rs. 3.3 lakh.Step 6: Required average selling price per remaining car = 3.3 lakh / 3 = Rs. 1.1 lakh. Verification / Alternative check: If each of the three remaining cars is sold for Rs. 1.1 lakh, revenue from them = 3 * 1.1 lakh = Rs. 3.3 lakh.Total revenue from all four cars = 1.2 lakh + 3.3 lakh = Rs. 4.5 lakh.Total profit = total revenue - total investment = 4.5 lakh - 3 lakh = Rs. 1.5 lakh, which is 50% of Rs. 3 lakh. Why Other Options Are Wrong: Average prices such as Rs. 1.5 lakh or Rs. 1.65 lakh would give profits higher than 50%. Values like Rs. 1.2 lakh or Rs. 1.3 lakh would yield total revenues that do not align exactly with a 50% overall profit. Only Rs. 1.1 lakh produces precisely the required 50% profit on the combined investment. Common Pitfalls: Some learners incorrectly compute profit on only the purchase cost of the cars and ignore repair expenses, underestimating total investment. Others mistakenly try to allocate equal profit per car instead of working from the total revenue target. Focusing on overall cost and total profit first makes the reasoning much clearer. Final Answer: The mechanic should sell each of the remaining three cars at an average price of Rs. 1.1 lakh.

Question 8

The marked price of an article is increased by 25%, and the selling price is increased by 16.66%, so that the amount of profit doubles. If the original marked price was Rs. 400 and this was 33.33% higher than the corresponding cost price, what is th…

Accepted Answer

Introduction / Context: This profit and loss question involves both a marked price (labelled price) and a selling price, with changes applied to each. The key condition is that the profit amount doubles after increasing both prices by given percentages. Combined with a relationship between marked price and cost price, the problem requires determining the new selling price. It tests multi-step percentage reasoning and equation setup. Given Data / Assumptions: Original marked price = Rs. 400. The original marked price is 33.33% (one-third) higher than cost price. Therefore, cost price CP is such that 400 = CP * (1 + 1 / 3). Marked price is increased by 25%. Selling price is increased by 16.66% (approximately one-sixth). As a result, the profit amount doubles. We must find the new increased selling price. Concept / Approach: First, we find the original cost price from the relation between marked price and cost price. Then we let the original selling price be S. Original profit = S - CP. After changes, marked price does not directly affect cost but indicates that the new selling price is 1.1666 times S (approximately 7 / 6 times S). The new profit is then new selling price minus CP, and this is given to be double the original profit. This yields an equation in S, which we can solve and then use to find the new selling price. Step-by-Step Solution: Step 1: Original marked price = Rs. 400 is 33.33% higher than CP, so 400 = CP * (4 / 3).Step 2: Therefore CP = 400 * 3 / 4 = Rs. 300.Step 3: Let original selling price be S. Then original profit = S - 300.Step 4: Selling price is increased by 16.66%, which is approximately 1 / 6, so new selling price = S * (1 + 1 / 6) = 7S / 6.Step 5: New profit = (7S / 6) - 300.Step 6: Given that the new profit is double the original profit, so (7S / 6) - 300 = 2(S - 300).Step 7: Simplify: 7S / 6 - 300 = 2S - 600. Multiply through by 6: 7S - 1800 = 12S - 3600.Step 8: Rearrange: 1800 = 5S, so S = 360.Step 9: New selling price = 7S / 6 = 7 * 360 / 6 = 7 * 60 = Rs. 420. Verification / Alternative check: Original profit = S - CP = 360 - 300 = Rs. 60.New profit with selling price Rs. 420: 420 - 300 = Rs. 120.The new profit is indeed double the original profit (120 compared to 60), confirming the correctness of S and the new selling price. Why Other Options Are Wrong: A new selling price of Rs. 360 is simply the original selling price and does not change profit. Rs. 240 would represent a loss relative to the cost price of Rs. 300. Rs. 480 or Rs. 600 would produce profit amounts much higher than double the original profit. Only Rs. 420 gives exactly double the original profit while matching the given percentage change. Common Pitfalls: Some learners try to double the profit percentage instead of doubling the absolute profit amount, which changes the problem. Others mistakenly apply the percentage increases to cost price rather than to marked price and selling price. It is also easy to round 16.66% incorrectly and introduce noticeable errors. Carefully distinguishing each base and working with exact fractions such as 1 / 3 and 1 / 6 avoids these issues. Final Answer: The increased selling price of the article is Rs. 420.

Question 9

A, B and C invest in a business in the ratio 3 : 4 : 5. The percentages of return on their investments are in the ratio 6 : 5 : 4 respectively. If B's earnings are Rs. 250 more than A's earnings, what is the total amount of earnings of A, B and C to…

Accepted Answer

Introduction / Context: This problem involves partners who invest in a business with different capital contributions and different percentage returns. Earnings for each partner depend on both their investment and their individual return percentage. The question asks for the total of all three earnings, given the difference between two of them. It is a good example of combining ratios multiplicatively. Given Data / Assumptions: Investment ratio of A : B : C = 3 : 4 : 5. Percentage return ratio of A : B : C = 6 : 5 : 4. B's earnings exceed A's earnings by Rs. 250. We must find the total earnings of A, B and C combined. Concept / Approach: Earnings of each partner are proportional to investment multiplied by percentage return. Thus, earnings are in the ratio (3 * 6) : (4 * 5) : (5 * 4). Once this combined ratio is known, the difference between B and A in this ratio can be matched to Rs. 250 to find the value of one ratio unit. Multiplying each ratio term by this unit gives individual earnings, and their sum gives the total earnings. Step-by-Step Solution: Step 1: Earnings are proportional to investment * return percentage.Step 2: Earnings ratio for A : B : C = 3 * 6 : 4 * 5 : 5 * 4 = 18 : 20 : 20.Step 3: Let the common earning unit be k. Then A earns 18k, B earns 20k, and C earns 20k.Step 4: B's earnings exceed A's by 20k - 18k = 2k, and this equals Rs. 250.Step 5: Therefore 2k = 250, so k = 125.Step 6: Earnings of A = 18k = 18 * 125 = Rs. 2250.Step 7: Earnings of B = 20k = 20 * 125 = Rs. 2500.Step 8: Earnings of C = 20k = 20 * 125 = Rs. 2500.Step 9: Total earnings = 2250 + 2500 + 2500 = Rs. 7250. Verification / Alternative check: Difference between B and A = 2500 - 2250 = Rs. 250, which matches the given condition.The ratio of A : B : C earnings is 2250 : 2500 : 2500. Dividing by 125 gives 18 : 20 : 20, confirming the combined ratio is correct. Why Other Options Are Wrong: Totals such as Rs. 6000 or Rs. 5000 would correspond to different values of k and therefore different earnings differences between A and B. Rs. 6500 also fails to produce a Rs. 250 difference between B and A when split in the ratio 18 : 20 : 20. Only Rs. 7250 ensures both the correct ratio and the Rs. 250 difference. Common Pitfalls: Some learners mistakenly add the ratios 3 : 4 : 5 and 6 : 5 : 4 instead of multiplying them term by term. Others equate the investment ratio alone to earnings and ignore the different return percentages. Remembering that earnings depend on both factors and treating them multiplicatively is the key insight. Final Answer: The total earnings of A, B and C together amount to Rs. 7250.

Question 10

A shopkeeper sells two articles for Rs. 1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. What is his overall percentage profit or loss on the two articles taken together?

Accepted Answer

Introduction / Context: This question illustrates a common trap in profit and loss: equal percentage profit and loss on equal selling prices does not result in zero net profit. The key issue is that profit and loss percentages are calculated on cost price, not on selling price, so the effective costs differ for the two articles. Given Data / Assumptions: Two articles are sold at Rs. 1000 each. On the first article, there is a profit of 20%. On the second article, there is a loss of 20%. We must find the overall percentage profit or loss on both articles together. Concept / Approach: Let cost prices of the first and second articles be C1 and C2. Given the profits and losses, selling price of each is Rs. 1000. For the first, 1000 = 1.20 * C1, and for the second, 1000 = 0.80 * C2. From these equations we compute C1 and C2, find total cost and total selling price, and then determine overall profit or loss percentage as (Total SP - Total CP) / Total CP * 100. Step-by-Step Solution: Step 1: For the first article, 1000 = 1.20 * C1, so C1 = 1000 / 1.20 = Rs. 833.33 approximately.Step 2: For the second article, 1000 = 0.80 * C2, so C2 = 1000 / 0.80 = Rs. 1250.Step 3: Total cost price = C1 + C2 = 833.33 + 1250 ≈ Rs. 2083.33.Step 4: Total selling price = 1000 + 1000 = Rs. 2000.Step 5: Overall profit or loss = Total SP - Total CP = 2000 - 2083.33 ≈ -83.33, which is a loss of Rs. 83.33.Step 6: Percentage loss = 83.33 / 2083.33 * 100 ≈ 4%. Verification / Alternative check: We can use fractions to be more exact. For the first article, C1 = 1000 / 1.2 = 1000 * 5 / 6 = 833 1/3 rupees.For the second article, C2 = 1000 / 0.8 = 1000 * 5 / 4 = 1250 rupees.Total cost = 2083 1/3 rupees, total SP = 2000 rupees.Loss = 83 1/3 rupees, so loss percentage = (83 1/3) / (2083 1/3) * 100 = 4% exactly. Why Other Options Are Wrong: Many people mistakenly choose “No profit no loss” because they see equal and opposite percentages, but that ignores the different bases. A 5% profit or 8% profit would require total SP to exceed total CP, which does not happen here. A 6% loss would imply a larger absolute loss than Rs. 83.33 on this total cost. Only a 4% loss fits the calculations. Common Pitfalls: The major pitfall is to assume that a gain of 20% and a loss of 20% simply cancel out. Another error is to average +20% and -20% to get 0%, which is not valid because the percentages apply to different cost prices. Always convert each case to cost price and then compute total profit or loss on the combined cost. Final Answer: The shopkeeper incurs an overall 4% loss on the two articles together.

Question 11

In what ratio should water and wine be mixed so that, when the mixture is sold at the cost price of pure wine, the seller makes a profit of 33.33% on the actual cost?

Accepted Answer

Introduction / Context: This mixture and profit question explores how adding free water to wine affects overall profit when the mixture is sold at the original cost price of pure wine. It tests understanding of how to relate profit percentage to the ratio of free component (water) to the costly component (wine). Given Data / Assumptions: Wine has some cost price per litre, say Rs. C. Water is free and has zero cost. The mixture is sold at the cost price of pure wine, i.e., selling price per litre of mixture = C. The desired profit percentage on the actual cost is 33.33%, which is approximately one-third. We must find the ratio water : wine in the mixture. Concept / Approach: Let the quantity of wine be W litres and water be A litres. Cost comes only from wine, so total cost = W * C. Total volume of mixture = W + A litres, and this is sold at C per litre. Thus, total revenue = (W + A) * C. Profit percentage is (Revenue - Cost) / Cost * 100. Setting this equal to 33.33% and simplifying leads to a relationship between A and W, from which the ratio water : wine can be found. Step-by-Step Solution: Step 1: Let wine quantity = W litres and water quantity = A litres.Step 2: Cost price of wine per litre = C, water is free.Step 3: Total cost = W * C.Step 4: Total mixture sold = W + A litres at price C per litre, so total revenue = (W + A) * C.Step 5: Profit = Revenue - Cost = (W + A) * C - W * C = A * C.Step 6: Profit percentage = (Profit / Cost) * 100 = (A * C) / (W * C) * 100 = (A / W) * 100.Step 7: Given profit percentage is 33.33% ≈ 1 / 3, so A / W = 1 / 3.Step 8: Therefore water : wine = A : W = 1 : 3. Verification / Alternative check: Assume W = 3 litres, A = 1 litre, and C = Rs. 10 per litre.Total cost = 3 * 10 = Rs. 30.Total mixture = 4 litres. Revenue at cost price C = 4 * 10 = Rs. 40.Profit = 40 - 30 = Rs. 10, profit percentage = 10 / 30 * 100 = 33.33%, confirming the mixture ratio. Why Other Options Are Wrong: Ratios such as 1 : 4, 2 : 3 or 3 : 4 yield different values of A / W and therefore produce profit percentages different from 33.33%. A ratio of 1 : 2 gives A / W = 1 / 2 or 50% profit. Only 1 : 3 corresponds to adding one-third as much water as wine, matching the required profit percentage. Common Pitfalls: Some learners invert the ratio and use wine : water instead of water : wine. Others mistakenly assume that 33.33% refers to the fraction of wine in the mixture rather than profit on cost. It is important to clearly distinguish between cost-bearing and free components and to base the profit calculation on cost. Final Answer: Water and wine should be mixed in the ratio 1 : 3 (water : wine).

Question 12

By mixing two qualities of pulses in the ratio 2 : 3 and selling the mixture at Rs. 22 per kilogram, a shopkeeper makes a profit of 10%. If the cost price of the cheaper quality is Rs. 14 per kilogram, what is the cost price per kilogram of the dear…

Accepted Answer

Introduction / Context: This question combines mixture and profit concepts. Two types of pulses with different cost prices are mixed in a given ratio and sold at a single price per kilogram with a known profit percentage. The goal is to determine the cost price of the more expensive quality using an average cost and profit relationship. Given Data / Assumptions: Two qualities of pulses are mixed in the ratio 2 : 3 (cheaper : dearer). Selling price of the mixture = Rs. 22 per kg. Profit on the mixture = 10%. Cost price of the cheaper quality = Rs. 14 per kg. We must find the cost price of the dearer quality. Concept / Approach: Let the cost price of the dearer pulses be x rupees per kg. For every 2 kg of cheaper pulses at Rs. 14 per kg and 3 kg of dearer pulses at Rs. x per kg, total cost and total quantity can be computed. The cost per kg of the mixture is then the total cost divided by 5 kg. Since the shopkeeper makes a 10% profit when selling at Rs. 22, the cost per kg must be 22 / 1.10. Setting this equal to the weighted average cost leads to an equation in x. Step-by-Step Solution: Step 1: Let the dearer pulses cost x rupees per kg.Step 2: Cost of 2 kg cheaper pulses = 2 * 14 = Rs. 28.Step 3: Cost of 3 kg dearer pulses = 3x rupees.Step 4: Total cost for 5 kg mixture = 28 + 3x.Step 5: Cost price per kg of mixture = (28 + 3x) / 5.Step 6: Selling price per kg = Rs. 22 with 10% profit, so cost price per kg = 22 / 1.10 = Rs. 20.Step 7: Set weighted average cost equal to 20: (28 + 3x) / 5 = 20.Step 8: Multiply both sides by 5: 28 + 3x = 100, so 3x = 72 and x = 24. Verification / Alternative check: With cheaper pulses at Rs. 14 and dearer at Rs. 24, cost for 2 kg cheaper = 28, for 3 kg dearer = 72, total = 100.Total quantity = 5 kg, so cost per kg = 100 / 5 = Rs. 20.Selling price per kg = Rs. 22, giving profit = 2 rupees per kg, or 2 / 20 * 100 = 10%. Why Other Options Are Wrong: At Rs. 23, weighted average cost would not equal Rs. 20. Rs. 25 would raise the average cost above 20, reducing profit percentage below 10 or eliminating profit altogether. Rs. 21 also fails to produce the correct 10% profit when the mixture is sold at Rs. 22. Therefore those values cannot be correct, and “None of these” is unnecessary since Rs. 24 is a direct match. Common Pitfalls: Some learners confuse the ratio 2 : 3 as a price ratio rather than a quantity ratio, or they treat 10% profit as a simple addition of Rs. 2 without verifying the base. Others may inadvertently use selling price instead of cost price when forming the average. Writing the total cost and total quantity explicitly, then linking to the required cost per kg, keeps the logic clear. Final Answer: The cost price of the dearer quality of pulses is Rs. 24 per kg.

Question 13

The sale price of an article including sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12% on the cost price (before tax), what is the cost price of the article?

Accepted Answer

Introduction / Context: This problem combines the concepts of profit and sales tax. The final amount paid by the customer includes tax on the selling price, while the shopkeeper's profit is calculated on the cost price. We are asked to reverse these steps and find the original cost price given the total bill and the tax and profit percentages. Given Data / Assumptions: Total amount paid by the customer (selling price plus sales tax) = Rs. 616. Sales tax rate = 10% of the shopkeeper's selling price before tax. Shopkeeper's profit on cost price = 12%. We must find the cost price of the article. Concept / Approach: Let CP be the cost price and SP be the selling price before adding tax. The shopkeeper makes a 12% profit, so SP = 1.12 * CP. Sales tax is 10% of SP, so the tax amount = 0.10 * SP, and the total amount paid by the customer is SP + 0.10 * SP = 1.10 * SP. This total is given as Rs. 616. We first find SP from this relation, then use SP = 1.12 * CP to recover CP. Step-by-Step Solution: Step 1: Let cost price be CP, selling price before tax be SP.Step 2: Given profit of 12%, SP = 1.12 * CP.Step 3: Sales tax at 10% means total amount paid = SP + 0.10 * SP = 1.10 * SP.Step 4: Given that 1.10 * SP = Rs. 616.Step 5: Therefore SP = 616 / 1.10 = Rs. 560.Step 6: Now SP = 1.12 * CP implies CP = SP / 1.12 = 560 / 1.12.Step 7: Compute CP: 1.12 = 112 / 100, so CP = 560 * 100 / 112 = 56000 / 112 = Rs. 500. Verification / Alternative check: With CP = Rs. 500, profit at 12% gives SP = 500 * 1.12 = Rs. 560.Sales tax at 10% on SP = 0.10 * 560 = Rs. 56.Total amount paid by customer = 560 + 56 = Rs. 616, which matches the figure in the question. Why Other Options Are Wrong: If CP were Rs. 560, SP at 12% profit would be larger than 560 and 10% tax on that would exceed Rs. 616. Values like Rs. 530, Rs. 514 or Rs. 480 similarly fail to produce a total of exactly Rs. 616 when 12% profit and 10% tax are correctly applied. Only CP = Rs. 500 passes the reverse calculation test. Common Pitfalls: Some learners mistakenly apply the 10% sales tax directly on the cost price instead of on the selling price. Others confuse profit percentage and tax percentage, adding or subtracting 10 and 12 directly from 616 without proper structure. Keeping track of the sequence (cost to selling price to taxed price) and basing each percentage on the correct amount is essential. Final Answer: The cost price of the article is Rs. 500.

Question 14

A milkman has 20 litres of pure milk and mixes 5 litres of free water into it; if the cost price of pure milk is Rs. 18 per litre, then what percentage profit does he earn by selling the entire 25 litre mixture at the same cost price per litre?

Accepted Answer

Introduction / Context: This aptitude question on profit and loss deals with adulteration, where a milkman mixes free water into pure milk and then sells the diluted mixture at the original cost price of milk. Problems of this type test understanding of cost price, selling price, effective quantity, and how mixing a free component like water increases profit percentage without changing the nominal selling price per litre. Given Data / Assumptions: The milkman initially has 20 litres of pure milk. He mixes 5 litres of water into the milk, and water is assumed to be free of cost. The cost price of pure milk is Rs. 18 per litre. He sells the entire mixture at Rs. 18 per litre, that is, at the original cost price of pure milk. There is no extra cost for water or mixing. We need to find the percentage profit earned on his actual cost. Concept / Approach: The key idea is that the cost is only for the milk, not for the water. By adding water, the milkman increases the total selling quantity while the total cost remains the same. Profit percentage is calculated as profit divided by cost price multiplied by 100. So we first compute the total cost of the 20 litres of milk, then compute the total selling price of the 25 litre mixture at Rs. 18 per litre, and finally compute the profit percentage from these values. Step-by-Step Solution: Step 1: Cost price of 1 litre of pure milk = Rs. 18.Step 2: Total volume of pure milk = 20 litres.Step 3: Total cost price of milk = 20 * 18 = Rs. 360.Step 4: Volume of water added = 5 litres (water is free, so no cost added).Step 5: Total volume of mixture = 20 + 5 = 25 litres.Step 6: Selling price per litre of mixture = Rs. 18 (same as milk cost price).Step 7: Total selling price of mixture = 25 * 18 = Rs. 450.Step 8: Profit = Selling price minus Cost price = 450 - 360 = Rs. 90.Step 9: Profit percentage = (Profit / Cost price) * 100 = (90 / 360) * 100.Step 10: Simplify the fraction 90 / 360 = 1 / 4.Step 11: Profit percentage = (1 / 4) * 100 = 25%. Verification / Alternative check: Another way is to think directly in terms of effective gain in quantity. The milkman paid for 20 litres but sells 25 litres. So the quantity gained over paid quantity is 5 litres on a base of 20 litres. As a fraction that is 5 / 20 = 1 / 4. Multiplying by 100 gives 25% effective gain. This matches the profit percentage computed using cost and selling price, which confirms that the answer is consistent and correct. Why Other Options Are Wrong: 20%: This would be correct if the gained quantity or profit were one fifth of the cost, but here the extra effective quantity is one fourth of the original quantity. 33.33%: This would correspond to a gain of one third of the cost price, which does not match the ratio of 5 litres to 20 litres. 18%: This is simply close to the cost price per litre (Rs. 18) but has no relation to the actual profit percentage. Common Pitfalls: Students sometimes mistakenly compute profit on 25 litres instead of 20 litres, which leads to wrong logic. Another common error is to treat the cost price per litre of the mixture as the same as that of milk without accounting for the added water being free, which hides the profit. Some learners confuse absolute profit in rupees with profit percentage, which must always be relative to the cost price. Final Answer: The milkman earns a profit of 25% by selling the mixture at the original cost price of pure milk.

Question 15

Bhajan Singh purchases 120 reams of paper at Rs. 80 per ream and also pays transport, octroi and coolie charges; if he wants an 8% profit on the whole lot, what should be his selling price per ream?

Accepted Answer

Introduction / Context: This question is a standard profit and loss problem involving overhead expenses. The buyer not only pays the basic cost price for each ream of paper but also pays additional costs like transportation, octroi and coolie charges. The effective cost price per unit must include all these overheads. Only after computing the total cost can we determine the selling price per ream that will give the desired profit percentage. Given Data / Assumptions: Number of reams purchased = 120. Basic cost price per ream = Rs. 80. Transportation cost = Rs. 280. Octroi rate = 40 paise (Rs. 0.40) per ream. Coolie charges = Rs. 72. Desired profit percentage on total cost = 8%. All reams are assumed to be sold at the same price per ream. Concept / Approach: The concept is to treat all expenses as part of the cost price. First we compute the total money spent on purchasing the paper and paying all related expenses. From this, we find the effective cost price per ream. Then, using the desired profit percentage, we compute the required selling price per ream. The formula used is: Required selling price per unit = Total cost * (1 + profit percentage / 100) divided by total number of units. Step-by-Step Solution: Step 1: Cost of 120 reams at Rs. 80 per ream = 120 * 80 = Rs. 9600.Step 2: Transportation cost = Rs. 280.Step 3: Octroi per ream = Rs. 0.40, so total octroi = 120 * 0.40 = Rs. 48.Step 4: Coolie charges = Rs. 72.Step 5: Total cost = 9600 + 280 + 48 + 72.Step 6: Compute the sum: 9600 + 280 = 9880; 9880 + 48 = 9928; 9928 + 72 = Rs. 10000.Step 7: Hence total cost price for the entire lot = Rs. 10000.Step 8: Desired profit = 8% of total cost.Step 9: Total selling price needed = 10000 * (1 + 8 / 100) = 10000 * 1.08 = Rs. 10800.Step 10: Selling price per ream = 10800 / 120.Step 11: 10800 / 120 = 90, so required selling price per ream = Rs. 90. Verification / Alternative check: To verify, we can check that selling at Rs. 90 per ream actually yields 8% profit. Total revenue = 120 * 90 = Rs. 10800. Profit = 10800 minus total cost 10000 = Rs. 800. Profit percentage = (800 / 10000) * 100 = 8%. This matches the required profit percentage, confirming that Rs. 90 per ream is correct. Why Other Options Are Wrong: Rs. 89: If he sells at Rs. 89, total revenue is 120 * 89 = Rs. 10680, giving a profit of only Rs. 680, which is 6.8% profit, not 8%. Rs. 87.48: This is close to the effective cost per ream if profit were lower, but using this value would give less than 8% profit. Rs. 86: At Rs. 86 per ream, total revenue is 120 * 86 = Rs. 10320, profit = Rs. 320, which equals only 3.2% profit. Common Pitfalls: Ignoring overheads like octroi and coolie charges and using only the basic purchase cost, which underestimates real cost price. Mistaking the profit percentage as applied per ream individually rather than on total cost. Carrying out division incorrectly when calculating the selling price per ream. Final Answer: Bhajan Singh should sell each ream at Rs. 90 to earn an 8% profit on his total investment.

Question 16

A dealer sells two cattle for Rs. 500 each, making a loss of 10% on one animal and a gain of 10% on the other; what is his overall percentage gain or loss on the entire transaction?

Accepted Answer

Introduction / Context: This profit and loss question illustrates an important concept: equal percentage gain and percentage loss on equal selling prices do not cancel out. Even though one item is sold at a 10% profit and the other at a 10% loss, the dealer does not break even. The overall result is a small net loss. Understanding why this happens is crucial for aptitude exams and real life business decisions. Given Data / Assumptions: The dealer sells two cattle. Selling price of each animal = Rs. 500. On one animal, there is a 10% loss. On the other animal, there is a 10% profit. We need to find the net percentage gain or loss on the combined transaction. Concept / Approach: Profit and loss percentages are calculated on cost price, not on selling price. If selling prices are equal but cost prices are different, equal percentages of profit and loss do not cancel each other. The usual approach is to compute the separate cost prices of both cattle using the known selling price and percentages, then sum these cost prices to find the total cost. Compare total cost with total selling price to find total profit or loss, and then compute the net percentage effect. Step-by-Step Solution: Step 1: Let the first animal be sold at a loss of 10%.Step 2: Selling price of the first animal = Rs. 500.Step 3: If loss is 10%, then selling price = 90% of cost price.Step 4: So cost price of first animal = 500 / 0.90 = Rs. 555.56 approximately.Step 5: For the second animal, there is a profit of 10%.Step 6: Selling price of the second animal = Rs. 500.Step 7: If profit is 10%, then selling price = 110% of cost price.Step 8: So cost price of second animal = 500 / 1.10 = Rs. 454.55 approximately.Step 9: Total cost price = 555.56 + 454.55 ≈ Rs. 1010.11.Step 10: Total selling price = 500 + 500 = Rs. 1000.Step 11: Net loss = Total cost price minus Total selling price ≈ 1010.11 - 1000 = Rs. 10.11 (approximately).Step 12: Loss percentage = (Net loss / Total cost price) * 100 ≈ (10.11 / 1010.11) * 100 ≈ 1% loss. Verification / Alternative check: A known result in aptitude is that if a trader gains x% on one sale and loses x% on another sale of equal cost price, the net effect is a loss of x^2 / 100 percent. However in this question the selling prices are equal, not the cost prices. Still, computing numerically as done above clearly shows a small loss. If we take exact fractions (500 / 0.9 and 500 / 1.1) and simplify using algebra, the percentage loss tends to approximately 1%. This reconfirms that the trader loses around 1% overall. Why Other Options Are Wrong: 10% loss: This would require the total selling price to be 10% less than the total cost price, which is not the case here. The loss is much smaller. 1% gain: This would mean total selling price is greater than total cost, which contradicts the calculations. Neither loss nor profit: Many students mistakenly choose this because gains and losses look symmetric, but profit and loss percentages work on different bases, so they do not cancel out. Common Pitfalls: Assuming that a 10% gain and a 10% loss will always cancel out and give no profit or loss. Calculating percentage changes incorrectly by using selling price instead of cost price as the base. Not adding cost prices correctly before comparing with total selling price, which can give a wrong impression about net profit or loss. Final Answer: The dealer suffers a net loss of about 1% loss on the entire transaction.

Question 17

In a festive scheme, a pack of three soaps with marked price Rs. 45 is sold for Rs. 42 and still gives the shopkeeper a profit of 5%; what is the cost price of the entire three-soap pack?

Accepted Answer

Introduction / Context: This question focuses on calculating cost price when selling price and profit percentage are known. The situation describes a promotional scheme where a pack of three soaps with a marked price is sold at a slightly reduced price, yet the shopkeeper still earns a profit. This type of problem is very common in commerce and aptitude tests, helping candidates understand the relationship between marked price, selling price, cost price and profit percentage. Given Data / Assumptions: Marked price of a pack of three soaps = Rs. 45. Selling price of the pack in the scheme = Rs. 42. Profit made by selling at Rs. 42 is 5% of the cost price. We assume no other additional charges or taxes. We are required to find the cost price of the entire three-soap pack. Concept / Approach: The key formula in profit and loss is: Selling price = Cost price * (1 + profit percentage / 100) when there is a profit. Here, we know the selling price and the profit percentage, so we can invert the formula to find the cost price. That is, Cost price = Selling price / (1 + profit percentage / 100). We do not actually need to use the marked price numerically, because the question directly connects profit to cost price and the given selling price of Rs. 42. Step-by-Step Solution: Step 1: Let the cost price of the pack be denoted by CP.Step 2: Profit percentage = 5%.Step 3: Selling price of the pack = Rs. 42.Step 4: Relation for profit: Selling price = Cost price * (1 + 5 / 100).Step 5: That means 42 = CP * 1.05.Step 6: So CP = 42 / 1.05.Step 7: Compute 42 / 1.05 = 4000 / 100 = Rs. 40 exactly.Step 8: Therefore, the cost price of the three-soap pack is Rs. 40. Verification / Alternative check: We can verify by calculating the profit once we assume cost price is Rs. 40. If CP = Rs. 40 and SP = Rs. 42, profit = 42 minus 40 = Rs. 2. Profit percentage = (2 / 40) * 100 = 5%. This exactly matches the given profit percentage. The marked price of Rs. 45 simply indicates that the shopkeeper is offering a Rs. 3 discount off the marked price, but the core calculations still satisfy the required profit condition. Why Other Options Are Wrong: Rs. 38: At this cost, profit would be 42 minus 38 = Rs. 4, which is more than 5% of 38. The profit percentage would be approximately 10.53%. Rs. 39: Profit would be Rs. 3 on cost 39, which is about 7.69%, not 5%. Rs. 41: Profit would be Rs. 1 on cost 41, which is about 2.44%, again not equal to 5%. Common Pitfalls: Using marked price instead of selling price in the profit formula and mixing up which value is the base. Applying the percentage directly to the selling price rather than to the cost price. Performing the division 42 / 1.05 incorrectly and rounding too early, which may lead to a slightly wrong answer. Final Answer: The cost price of the three-soap pack that gives a 5% profit when sold for Rs. 42 is Rs. 40.

Question 18

Rahul buys a Nokia mobile handset; the shopkeeper offers a 5% discount on the actual sale price and Rahul pays Rs. 3325 without tax, also avoiding a 20% tax that would have been charged on the billed amount; what is the total amount of discount and …

Accepted Answer

Introduction / Context: This profit and loss question combines discount and tax calculation. Rahul negotiates a discount on the mobile phone and also manages to avoid paying tax that would normally be applied if he asked for a bill. The objective is to compare what he actually pays with what he would have paid without discount and with tax, and then compute the total benefit in rupees. Understanding such questions is useful for both competitive exams and day to day shopping decisions. Given Data / Assumptions: Let the actual sale price or list price of the mobile be P rupees. The shopkeeper offers a 5% discount on this price. Rahul finally pays Rs. 3325 without any tax. If Rahul had insisted on a bill, he would have had to pay 20% tax. The 20% tax is applied on the sale price (without discount) under usual interpretation. We need to find the total amount of benefit Rahul gains, combining both discount and avoided tax. Concept / Approach: First, we use the discount information to compute the original list price P. If Rahul receives a 5% discount and pays Rs. 3325, then 3325 is equal to 95% of P. Once we find P, we calculate the amount that would have been payable under normal conditions, that is, full price plus 20% tax. Finally, we compare that full amount with the 3325 actually paid to get the total discount and tax saved. The difference between these two amounts is exactly the benefit Rahul receives. Step-by-Step Solution: Step 1: Let the original sale price of the mobile be P.Step 2: Rahul gets a 5% discount, so he pays 95% of P.Step 3: Therefore, 0.95 * P = 3325.Step 4: Solve for P: P = 3325 / 0.95.Step 5: Compute P: 3325 / 0.95 = 3500. So the list price of the mobile is Rs. 3500.Step 6: If no discount and with tax, Rahul would pay the full list price plus 20% tax.Step 7: Tax at 20% on 3500 = 3500 * 0.20 = Rs. 700.Step 8: Hence, the amount payable with bill and without discount = 3500 + 700 = Rs. 4200.Step 9: Rahul actually pays Rs. 3325 without tax.Step 10: Total benefit (discount plus tax saved) = 4200 - 3325.Step 11: Compute the difference: 4200 - 3325 = Rs. 875. Verification / Alternative check: We can separately identify the discount and tax components. Discount amount = 5% of 3500 = 0.05 * 3500 = Rs. 175. Potential tax he avoided = 20% of 3500 = Rs. 700. Sum of these savings = 175 + 700 = Rs. 875. This total matches the earlier difference between full payment with tax and his actual payment. Therefore, both reasoning paths yield the same amount, confirming that the answer is correct and consistent. Why Other Options Are Wrong: Rs. 750: This could arise from adding only the tax saved and an incorrect value for discount, but it does not match proper calculations. Rs. 375: This is too small, close to only part of the discount or a miscalculated combined benefit. Rs. 525: This could come from incorrect interpretation of how tax and discount interact, but again it does not match the actual numbers. Common Pitfalls: Applying the 20% tax on the discounted price instead of the full list price, which changes the interpretation of the question. Forgetting that Rahul saves both the discount amount and the full tax amount, not just one of them. Miscomputing the list price from the discounted payment by not dividing by 0.95 correctly. Final Answer: Rahul gains a total benefit of Rs. 875 through the combination of discount and avoided tax.

Question 19

A retailer buys a radio for Rs. 225, incurs overhead expenses of Rs. 15 and sells the radio for Rs. 300; what is his percentage profit on the effective cost price?

Accepted Answer

Introduction / Context: This question tests the understanding of effective cost price when overhead expenses are involved. A retailer not only pays the purchase price of an item but also additional expenses such as packing, transport or local handling. These extra costs must be added to the basic cost to get the true cost price. The profit percentage is then calculated using this combined cost price and the final selling price. Given Data / Assumptions: Basic cost price of the radio = Rs. 225. Overhead expenses (for example, transport, shop expenses) = Rs. 15. Final selling price of the radio = Rs. 300. No other hidden costs or taxes are given. We need to calculate the profit percentage based on total cost. Concept / Approach: The total cost price (effective CP) is the sum of the basic purchase cost and the overhead expenses. Profit is the difference between selling price and this effective cost price. Once the profit amount is known, profit percentage is calculated using the formula: Profit percentage = (Profit / Cost price) * 100. The entire computation focuses on correctly identifying the cost base, which includes both the radio price and overhead expenses. Step-by-Step Solution: Step 1: Basic cost price of the radio = Rs. 225.Step 2: Overhead expenses = Rs. 15.Step 3: Effective cost price (CP) = 225 + 15 = Rs. 240.Step 4: Selling price (SP) of the radio = Rs. 300.Step 5: Profit = SP - CP = 300 - 240 = Rs. 60.Step 6: Profit percentage = (Profit / CP) * 100.Step 7: Substitute the values: Profit percentage = (60 / 240) * 100.Step 8: Simplify 60 / 240 = 1 / 4.Step 9: Hence profit percentage = (1 / 4) * 100 = 25%. Verification / Alternative check: We can check quickly by using the idea that a 25% profit means the selling price is 125% of the cost price. If the cost price is Rs. 240, then 125% of 240 is 240 * 1.25 = 300. Since the given selling price is exactly Rs. 300, the calculation aligns perfectly with a 25% profit, confirming the result. Why Other Options Are Wrong: 10%: A 10% profit on Rs. 240 would be Rs. 24, giving a selling price of Rs. 264, which is far less than Rs. 300. 50%: A 50% profit on Rs. 240 would mean a profit of Rs. 120 and a selling price of Rs. 360, which does not match the data. 52%: This is just a distractor and does not correspond to any correct calculation based on the given values. Common Pitfalls: Computing profit percentage using only the basic purchase price of Rs. 225, ignoring the Rs. 15 overhead, which overstates the profit percentage. Accidentally subtracting overhead costs from selling price rather than adding them to the cost price. Making arithmetic mistakes when simplifying the fraction 60 / 240. Final Answer: The retailer makes a profit of 25% on the effective cost price of the radio.

Question 20

A milkman has 20 litres of pure milk and adds 5 litres of free water to it; if the cost price of pure milk is Rs. 18 per litre and he sells the entire 25 litre mixture at Rs. 18 per litre, what is his profit percentage?

Accepted Answer

Introduction / Context: This is another classic mixture and profit question involving adulteration with water. The milkman increases the volume of what he sells by mixing water, which has no cost. He still charges the same rate per litre as for pure milk. Such scenarios are common in aptitude tests to check whether the learner can correctly separate cost bearing components from free components and then compute the resulting profit percentage. Given Data / Assumptions: Initial quantity of pure milk = 20 litres. Quantity of water added = 5 litres. Total quantity after mixing = 25 litres. Cost price of pure milk per litre = Rs. 18. Water is free and does not add to the cost. The mixture of 25 litres is sold at Rs. 18 per litre. We need to find the profit percentage on the milkman cost. Concept / Approach: The milkman pays only for the milk, not for the water. Profit arises because he sells more litres than he actually paid for. First, find the total cost of the milk. Then, calculate the total selling price of the mixture. The difference between total selling price and total cost gives the profit in rupees. Finally compute profit percentage using profit divided by cost price multiplied by 100. This is the standard approach in adulteration type questions. Step-by-Step Solution: Step 1: Cost price of 1 litre of milk = Rs. 18.Step 2: Quantity of milk = 20 litres.Step 3: Total cost of milk = 20 * 18 = Rs. 360.Step 4: Quantity of water added = 5 litres, cost of water = Rs. 0.Step 5: Total mixture quantity = 20 + 5 = 25 litres.Step 6: Selling price per litre of mixture = Rs. 18.Step 7: Total selling price = 25 * 18 = Rs. 450.Step 8: Profit = 450 - 360 = Rs. 90.Step 9: Profit percentage = (Profit / Cost price) * 100.Step 10: Profit percentage = (90 / 360) * 100.Step 11: Simplify 90 / 360 = 1 / 4, so profit percentage = 25%. Verification / Alternative check: An intuitive way to confirm is to consider that the milkman paid for only 20 litres but sells 25 litres. Free extra litres = 5. The free quantity as a fraction of the original paid quantity is 5 / 20 = 1 / 4. Therefore, the gain on cost is 25%. This matches the detailed calculation, confirming the correctness of the result. Why Other Options Are Wrong: 20%: This would imply that free quantity is one fifth of the paid quantity, which is not true here because 5 is not one fifth of 20. 33.33%: That suggests a free quantity equal to one third of cost basis. However 5 is not one third of 20. 18%: This is unrelated to the ratio of free quantity to paid quantity and does not match the computed profit. Common Pitfalls: Using the total quantity 25 litres as the cost base instead of the original 20 litres paid for. Thinking that selling at cost price per litre always gives zero profit, ignoring the effect of added free water. Confusing absolute profit in rupees with profit percentage on cost. Final Answer: The milkman earns a profit of 25% by mixing water and selling the mixture at the original cost price per litre.

Profit and Loss Questions