Question 1

If the selling price of 40 articles is equal to the cost price of 50 articles of the same kind, what is the percentage gain or loss in the transaction?

Accepted Answer

Introduction / Context: This is a classic profit and loss question based purely on ratios of quantities. The relationship between the selling price of a certain number of articles and the cost price of a different number of the same articles directly gives the profit or loss percentage, without needing any actual rupee values. Given Data / Assumptions: Selling price of 40 articles (SP40) equals cost price of 50 articles (CP50). All articles are identical and have the same cost price per unit. We must decide whether there is a gain or loss and then calculate the percentage. Concept / Approach: Let the cost price per article be C and the selling price per article be S. Then total cost for 50 articles is 50C, and total selling price for 40 articles is 40S. Given 40S = 50C, we get a direct relationship between S and C. The profit or loss per article is S - C. Expressing this as a percentage of C gives the required profit or gain percentage. Step-by-Step Solution: Let CP per article = C and SP per article = S. Given 40S = 50C. Divide both sides by 10 to simplify: 4S = 5C. So S = (5/4) * C = 1.25C. Profit per article = S - C = 1.25C - C = 0.25C. Profit percentage = (0.25C / C) * 100 = 25% gain. Verification / Alternative check: Take a simple numeric example. Assume C = Rs 4; then from S = (5/4) * C, we get S = Rs 5. Selling 40 articles at Rs 5 each gives SP40 = 200 rupees. Cost of 50 articles is 50 * 4 = 200 rupees. This satisfies the condition that SP40 equals CP50 and clearly indicates that S is greater than C, implying profit. The percentage profit is (5 - 4)/4 * 100 = 25%. Why Other Options Are Wrong: If profit were 20%, then S would be 1.20C which does not satisfy the 40S = 50C relationship. Loss options are incorrect because the selling price is higher than the cost price per unit; hence there is gain, not loss. Common Pitfalls: One common error is to reverse the ratio and assume 40C = 50S. Another mistake is to compare 40 and 50 directly and think the percentage is 20% simply from the difference in quantities. Always express SP and CP in terms of the same per unit base variable before computing percentages. Final Answer: The trader makes a 25% gain in this transaction.

Question 2

When an African safari ticket is sold with a discount of 20% on its marked price, the seller makes a profit of 43%. If instead the discount allowed is 28%, what will be the new percentage profit?

Accepted Answer

Introduction / Context: This question links marked price, discount percentage, and profit percentage. It first gives a scenario where a certain discount results in a known profit. Then it changes the discount and asks for the new profit percentage, assuming cost price remains the same. This is a common pattern in retail profit and loss questions. Given Data / Assumptions: Marked price (MP) of the ticket is some value M. With a 20% discount, profit is 43%. With a 28% discount, cost price (CP) is unchanged and we must find the new profit percentage. No extra costs such as taxes are considered. Concept / Approach: First, express the selling price after 20% discount in terms of M, then relate it to cost price using the 43% profit. This allows us to find CP in terms of M. Next, compute the selling price with 28% discount and use the same CP to calculate the new profit percentage: Profit% = (SP2 - CP) / CP * 100. Step-by-Step Solution: Let the marked price be M. With 20% discount, selling price SP1 = 0.80M. Profit on SP1 is 43%, so SP1 = CP * 1.43 → CP = SP1 / 1.43 = 0.80M / 1.43. With 28% discount, selling price SP2 = 0.72M. Profit percentage with SP2 is: Profit% = [(SP2 - CP) / CP] * 100. Substitute CP: Profit% = [(0.72M - 0.80M/1.43) / (0.80M/1.43)] * 100. Simplify the fraction to obtain profit percentage ≈ 28.7%. Verification / Alternative check: Choose a convenient marked price, say M = Rs 143. Then SP1 = 0.80 * 143 = Rs 114.40. Since profit is 43%, CP = 114.40 / 1.43 = Rs 80. With 28% discount, SP2 = 0.72 * 143 = Rs 102.96. Profit = 102.96 - 80 = Rs 22.96. Profit percentage = (22.96 / 80) * 100 ≈ 28.7%. This numerical check confirms the derived result. Why Other Options Are Wrong: 71% and 113.3% are far higher than 43% and do not match the computation. A profit of 13.6% is too low given that the discount is only slightly higher than before and the initial profit was already 43%. Only 28.7% fits the exact calculations. Common Pitfalls: A typical error is to treat profit percentage directly on marked price instead of cost price. Another mistake is to subtract discount percentages or profit percentages directly without recalculating selling price and cost price. Always recompute CP from the first scenario before working out the effect of the new discount. Final Answer: With a 28% discount, the new profit percentage is approximately 28.7 percent.

Question 3

A shopkeeper sells dried apricots at Rs 1210 per kg and suffers a loss of 12%. If the shopkeeper decides to sell them at Rs 1331 per kg instead, what will be the percentage profit or loss?

Accepted Answer

Introduction / Context: In this question, a shopkeeper first sells dried apricots at a price which leads to a known loss percentage. Then the selling price is increased, and we must determine the new profit or loss percentage. The key idea is to find the cost price from the first scenario and then compare it with the new selling price. Given Data / Assumptions: Initial selling price SP1 = Rs 1210 per kg. Loss at SP1 is 12%. New selling price SP2 = Rs 1331 per kg. We assume cost price per kg remains constant. We need to find the percentage profit or loss at SP2. Concept / Approach: Loss of 12% means SP1 = 0.88 * CP. From this, CP can be calculated as CP = SP1 / 0.88. Once cost price is known, we calculate Profit or Loss at the new selling price using Profit or Loss = SP2 - CP, and then express it as a percentage of CP. A negative value indicates loss while a positive value indicates profit. Step-by-Step Solution: Given SP1 = Rs 1210 and loss = 12%, so SP1 = 0.88 * CP. Thus CP = 1210 / 0.88 = Rs 1375. New selling price SP2 = Rs 1331. Difference between SP2 and CP = 1331 - 1375 = -44, which indicates a loss of Rs 44 per kg. Loss percentage = (44 / 1375) * 100 ≈ 3.2%. So the shopkeeper now suffers a loss of approximately 3.2%. Verification / Alternative check: Reversing the steps, with CP = Rs 1375, at SP1 = Rs 1210 the loss is 1375 - 1210 = Rs 165. Loss percentage is (165 / 1375) * 100 = 12%, which matches the given data. For SP2 = Rs 1331, loss is 1375 - 1331 = Rs 44. A percentage calculation confirms about 3.2% loss, so the CP is consistent and the new loss percentage is correct. Why Other Options Are Wrong: 6.4 percent loss or gain are obtained if someone mistakenly doubles the 3.2% or miscalculates CP. 3.2 percent gain is incorrect because SP2 is still less than CP, indicating a loss, not a gain. Only 3.2 percent loss matches the correct numerical analysis. Common Pitfalls: Students sometimes treat 1210 as cost price and incorrectly compute profit from there. Another error is to apply the 12% directly on 1210 instead of relating it to cost price. Also, mixing up profit and loss signs can lead to calling a loss a gain. Final Answer: At the new selling price of Rs 1331 per kg, the shopkeeper incurs a loss of approximately 3.2 percent.

Question 4

When a discount of 20% is given on a movie ticket, the seller makes a profit of 34%. If instead the discount is 15%, what will be the new percentage profit?

Accepted Answer

Introduction / Context: This question is another example involving marked price, discount, and profit. Initially a 20% discount produces a profit of 34%. The discount is then reduced to 15%, and we must determine the new profit percentage given that the cost price does not change. Such problems appear frequently in profit and loss sections of aptitude tests. Given Data / Assumptions: Marked price (MP) of the movie ticket is some value M. With 20% discount, profit is 34%. With 15% discount, cost price remains the same. We must compute new profit percentage with a 15% discount. Concept / Approach: First scenario: SP1 = 0.80M (due to 20% discount). This SP1 corresponds to a 34% profit on cost price: SP1 = 1.34 * CP, so CP = SP1 / 1.34 = 0.80M / 1.34. Second scenario: SP2 = 0.85M (due to 15% discount). Using the same CP, profit percentage with SP2 is (SP2 - CP) / CP * 100. Substituting CP in terms of M gives the exact new profit percentage. Step-by-Step Solution: Let MP = M. With 20% discount, SP1 = 0.80M. Given profit = 34%, so SP1 = 1.34 * CP → CP = 0.80M / 1.34. With 15% discount, SP2 = 0.85M. New profit percentage = [(SP2 - CP) / CP] * 100. Substitute CP: Profit% = [(0.85M - 0.80M/1.34) / (0.80M/1.34)] * 100. Simplify the expression to obtain profit% ≈ 42.375%. Verification / Alternative check: Choose M = Rs 134 for convenience. Then SP1 = 0.80 * 134 = Rs 107.2. Given SP1 is 34% above CP, CP = 107.2 / 1.34 = Rs 80. With 15% discount, SP2 = 0.85 * 134 = Rs 113.9. Profit = 113.9 - 80 = Rs 33.9 and profit percentage = (33.9 / 80) * 100 ≈ 42.375%, confirming the result. Why Other Options Are Wrong: 49% and 55.625% are significantly higher than the calculated value and would correspond to very small cost prices. A profit of 35.75% is only slightly above 34% and does not match the precise calculation. Only 42.375% is consistent with the algebraic and numerical computations. Common Pitfalls: A common mistake is to subtract or add discount percentages directly without recomputing selling price. Another is to assume profit percentage changes linearly with discount. Some students also confuse profit on marked price with profit on cost price, leading to wrong equations. Final Answer: With a 15% discount, the new profit percentage becomes approximately 42.375 percent.

Question 5

A store sells a watch at a profit equal to 25% of its cost price. What is the percentage of profit when measured as a percentage of the selling price?

Accepted Answer

Introduction / Context: This is a conceptual profit and loss question that checks your understanding of the difference between expressing profit as a percentage of cost price and expressing profit as a percentage of selling price. The numerical value of profit remains the same, but the base for the percentage calculation changes. Given Data / Assumptions: Profit is 25% of cost price (CP). We must find profit percentage with respect to selling price (SP). The watch is a single item, so we can use one CP and one SP. Concept / Approach: If profit is 25% of CP, then profit = 0.25 * CP. Selling price is CP plus profit, SP = CP + 0.25CP = 1.25CP. Profit as a percentage of SP is then (profit / SP) * 100. Since SP is greater than CP, the profit percentage relative to SP will be smaller than 25%. Step-by-Step Solution: Let CP = 100 units. Profit = 25% of CP = 25 units. Selling price SP = CP + profit = 100 + 25 = 125 units. Profit as a percentage of SP = (25 / 125) * 100. Simplify: 25 / 125 = 1 / 5. Thus profit percentage relative to SP = (1 / 5) * 100 = 20%. Verification / Alternative check: Using algebra, if profit = 0.25CP, then SP = 1.25CP. Profit% on SP = (0.25CP / 1.25CP) * 100 = (0.25 / 1.25) * 100 = (1 / 5) * 100 = 20%. This confirms the use of any assumed CP, such as 100, gives the same result. Why Other Options Are Wrong: 22%, 18%, and 15% are simply distractors. They do not arise from correct manipulation of profit and selling price. Only 20% satisfies the relationship between a 25% profit on cost price and the equivalent profit percentage on selling price. Common Pitfalls: Some learners forget to change the base when switching from profit on cost price to profit on selling price, and they incorrectly answer 25%. Others may incorrectly subtract a fixed number instead of recalculating the ratio. Always remember that percentage is relative to the base value used. Final Answer: The profit is 20% when expressed as a percentage of the selling price.

Question 6

A shopkeeper sells 17 Omega watches and earns a total profit equal to the selling price of 7 Omega watches. What is the shopkeeper's profit percentage?

Accepted Answer

Introduction / Context: This question involves interpreting a profit statement in terms of total selling price and cost price. The seller sells several identical items and is told that the total profit equals the selling price of a certain number of items. From this relationship, we can deduce the cost price per item and hence the profit percentage. Given Data / Assumptions: Total watches sold = 17 Omega watches. Total profit earned equals the selling price of 7 watches. All watches are identical with the same cost price and selling price per piece. We need to find overall profit percentage. Concept / Approach: Let S be the selling price per watch and C be the cost price per watch. Then total selling price for 17 watches is 17S and total cost is 17C. Given that the total profit is equal to selling price of 7 watches, profit = 7S. But profit is also 17S - 17C. Equating 17S - 17C to 7S allows us to find a relationship between S and C and hence compute profit percentage. Step-by-Step Solution: Let S = selling price per watch, C = cost price per watch. Total SP for 17 watches = 17S. Total CP for 17 watches = 17C. Profit = total SP - total CP = 17S - 17C. Given profit = 7S, so 17S - 17C = 7S. Rearrange: 17S - 7S = 17C → 10S = 17C. So C = (10/17)S → profit per watch = S - C = S - (10/17)S = (7/17)S. Profit percentage on cost = [(S - C) / C] * 100 = [(7/17)S / (10/17)S] *100 = (7/10)*100 = 70%. Verification / Alternative check: Assume S = Rs 17 so that S is a multiple of 17. Then C = (10/17)*17 = Rs 10. Profit per watch = 17 - 10 = Rs 7. For 17 watches, total profit = 17 * 7 = Rs 119. Selling price of 7 watches = 7 * 17 = Rs 119, which matches the given condition. Profit percentage = (7 / 10) * 100 = 70%, confirming the calculation. Why Other Options Are Wrong: 41.1 percent and 82.2 percent are distractor values that could appear from misinterpreting ratios or dividing incorrectly. 12.2 percent is far too small given that profit equals nearly half of total selling price for the 17 watches. Common Pitfalls: A typical mistake is to assume profit is equal to cost price of 7 watches, rather than selling price. Another common error is to solve the equation incorrectly and then compute profit percentage using the wrong base. Careful reading and algebra are essential. Final Answer: The shopkeeper's profit percentage is 70 percent.

Question 7

A shopkeeper sells 13 Titan watches and earns a total profit equal to the selling price of 3 Titan watches. What is the shopkeeper's profit percentage?

Accepted Answer

Introduction / Context: This problem mirrors the previous one, but with different numbers. It again tests your ability to interpret profit information in terms of the selling price of some of the items and to convert that relationship into a profit percentage on cost price. Given Data / Assumptions: Total watches sold = 13 Titan watches. Total profit equals the selling price of 3 watches. All watches have the same cost price and selling price per piece. We need to find the profit percentage on cost price. Concept / Approach: Let S be selling price per watch and C be cost price per watch. Total selling price for 13 watches is 13S, and total cost is 13C. Profit is 13S - 13C and is given to be equal to 3S. Equating these gives a linear equation relating S and C. From that equation, we determine the profit per watch and then the profit percentage on cost price. Step-by-Step Solution: Let S = selling price per watch and C = cost price per watch. Total SP for 13 watches = 13S. Total CP for 13 watches = 13C. Profit = 13S - 13C. Given profit = 3S, so 13S - 13C = 3S. Rearrange: 13S - 3S = 13C → 10S = 13C. Thus C = (10/13)S. Profit per watch = S - C = S - (10/13)S = (3/13)S. Profit percentage on cost = [(S - C) / C] * 100 = [(3/13)S / (10/13)S] * 100 = (3/10) * 100 = 30%. Verification / Alternative check: Assume S = Rs 13. Then C = (10/13) * 13 = Rs 10. Profit per watch = 13 - 10 = Rs 3. Total profit on 13 watches = 13 * 3 = Rs 39. Selling price of 3 watches = 3 * 13 = Rs 39, which satisfies the condition. Profit percentage = (3 / 10) * 100 = 30%, confirming the answer. Why Other Options Are Wrong: 23 percent, 46 percent, and 16 percent arise from possible misoperations with 10 and 13. However only 30 percent follows from the correct ratio C = (10/13)S and the resulting profit per watch. Common Pitfalls: Some candidates misread the statement and think profit equals cost price of 3 watches instead of selling price, which changes the equation. Others divide by the wrong number or compute profit percentage on selling price instead of cost price. Final Answer: The shopkeeper's profit percentage is 30 percent.

Question 8

A wholesaler sells a jacket to a retailer at a profit of 5%, and the retailer sells it to a customer at a further profit of 10%. If the customer pays Rs 4158 for the jacket, what was the cost price of the jacket for the wholesaler?

Accepted Answer

Introduction / Context: This chained profit question involves two levels of selling: from wholesaler to retailer and from retailer to final customer. Each level has its own profit percentage. We are given the final selling price to the customer and must work backwards to find the original cost price for the wholesaler. Given Data / Assumptions: The wholesaler sells the jacket to the retailer at a profit of 5%. The retailer sells the jacket to the customer at a profit of 10%. The final customer pays Rs 4158. There are no extra expenses other than the profit margins specified. We need the cost price for the wholesaler. Concept / Approach: If CPw is the cost price for the wholesaler, then the wholesaler sells at 1.05 * CPw to the retailer. Let CPr be the cost price for the retailer, so CPr = 1.05 * CPw. The retailer then sells to the final customer at 1.10 * CPr. The final selling price equals 4158. Combining these two multiplicative factors gives the total factor from CPw to final SP as 1.05 * 1.10 = 1.155. Step-by-Step Solution: Let CPw = x rupees. Wholesaler sells to retailer at 5% profit: CPr = 1.05x. Retailer sells to customer at 10% profit: SP = 1.10 * CPr = 1.10 * 1.05x = 1.155x. Given SP = 4158, so 1.155x = 4158. Thus x = 4158 / 1.155 = 3600 rupees. Verification / Alternative check: With CPw = Rs 3600, wholesaler sells at 5% profit: 3600 * 1.05 = Rs 3780. Retailer sells at 10% profit: 3780 * 1.10 = Rs 4158. This matches the given final price, confirming that the cost price to the wholesaler must be Rs 3600. Why Other Options Are Wrong: If CPw were 3500, 3400, or 3300 rupees, multiplying by 1.155 would yield final prices of 4042.5, 3927, and 3811.5 respectively, none of which is 4158. Therefore those options do not satisfy the relation between profits and final selling price. Common Pitfalls: Some learners mistakenly add percentages instead of multiplying by successive factors, treating the total profit as 15% of wholesaler cost price directly, which is not correct here because of compounding. Always convert each profit percentage into a multiplicative factor and apply them in sequence. Final Answer: The cost price of the jacket for the wholesaler was Rs 3600.

Question 9

The selling price of 6 bananas is equal to the cost price of 8 bananas of the same quality. What is the percentage profit made by the seller?

Accepted Answer

Introduction / Context: Here we again have a ratio based profit and loss question involving identical items. The relationship between selling price of 6 bananas and cost price of 8 bananas directly leads to the profit percentage without needing actual rupee amounts. Given Data / Assumptions: Selling price of 6 bananas (SP6) equals cost price of 8 bananas (CP8). All bananas have the same cost price C and selling price S per piece. We must compute profit percentage on cost price. Concept / Approach: Let cost price per banana be C and selling price per banana be S. Given 6S = 8C. From this relationship we find S in terms of C. Profit per banana is S - C. Profit percentage is (S - C) / C * 100. Because the quantities differ, there will be a profit, not a loss, as selling price per piece will be greater than cost price per piece. Step-by-Step Solution: Let CP per banana = C, SP per banana = S. Given 6S = 8C. Divide both sides by 2: 3S = 4C. So S = (4/3)C. Profit per banana = S - C = (4/3)C - C = (1/3)C. Profit percentage = [(1/3)C / C] * 100 = (1/3)*100 ≈ 33 1/3%. Verification / Alternative check: Assume C = Rs 3. Then S = (4/3)*3 = Rs 4. Cost of 8 bananas = 8 * 3 = Rs 24. Selling price of 6 bananas = 6 * 4 = Rs 24, which matches the condition. Profit per banana = 4 - 3 = Rs 1 and profit percentage = (1 / 3) * 100 ≈ 33.33%, confirming the answer. Why Other Options Are Wrong: 20%, 25%, and 30% come from miscalculations or confusion about which quantity is larger. The ratio 6 : 8 simplifies to 3 : 4 and directly leads to the fraction 1/3 for profit on cost. Only 33 1/3% is consistent. Common Pitfalls: A typical error is to invert the ratio and write 6C = 8S, which leads to a loss. Another error is to think that profit percentage is (8 - 6)/8 * 100, which ignores the fact that the equation involves price, not quantity alone. Always express SP and CP per unit before computing percentage. Final Answer: The seller makes a profit of 33 1/3 percent.

Question 10

A man sells an article at a profit of 15%. If he had sold it for Rs 6 more, he would have gained 18%. What was the cost price of the article, in rupees?

Accepted Answer

Introduction / Context: This classic profit and loss question compares two close selling prices for the same article, each linked to a different profit percentage. The difference between selling prices is a small fixed amount. Using this information, we build an equation to determine the unknown cost price. Given Data / Assumptions: First selling price SP1 gives a profit of 15%. Second selling price SP2 is Rs 6 higher than SP1 and gives a profit of 18%. Cost price CP is the same in both cases. We must find CP in rupees. Concept / Approach: Let CP = x. Then SP1 = x * 1.15 and SP2 = x * 1.18. Given that SP2 is Rs 6 more than SP1, we write x * 1.18 = x * 1.15 + 6. Solving this simple linear equation yields the cost price. This method uses the difference between the two profit percentages and the absolute rupee difference between the selling prices. Step-by-Step Solution: Let CP = x rupees. First selling price SP1 = 1.15x. Second selling price SP2 = 1.18x. Given SP2 = SP1 + 6, so 1.18x = 1.15x + 6. Rearrange: 1.18x - 1.15x = 6 → 0.03x = 6. Thus x = 6 / 0.03 = 200 rupees. Verification / Alternative check: With CP = Rs 200, SP1 = 1.15 * 200 = Rs 230 and SP2 = 1.18 * 200 = Rs 236. The difference SP2 - SP1 = 236 - 230 = Rs 6, which matches the problem statement. Profit at SP1 = 230 - 200 = 30 rupees, which is 15% of 200. Profit at SP2 = 236 - 200 = 36 rupees, which is 18% of 200. All conditions are satisfied. Why Other Options Are Wrong: If CP were 100 or 150 or 250, the difference between 15% and 18% of CP would not equal 6 rupees. Only CP = 200 makes the 3% difference equal to exactly 6 rupees, because 3% of 200 is 6. Common Pitfalls: Many learners fail to notice that the difference between 18% and 15% is 3% and that this difference, when multiplied by CP, must equal Rs 6. Instead they might try random substitution without building a clean algebraic equation. Careless arithmetic with percentages also leads to errors. Final Answer: The cost price of the article was Rs 200.

Question 11

If the ratio of the cost price to the selling price of an article is 4 : 5, what is the percentage profit on the article?

Accepted Answer

Introduction / Context: This question reverses the usual profit calculation. Instead of giving the profit percentage directly, it provides the ratio between cost price and selling price and asks for the profit percentage. Converting such ratios into percentages is very common in aptitude exams. Given Data / Assumptions: Ratio of cost price (CP) to selling price (SP) is 4 : 5. We need to find profit percentage on cost price. The article is a single item with one CP and one SP. Concept / Approach: A ratio CP : SP = 4 : 5 can be interpreted as CP = 4k, SP = 5k for some positive constant k. Profit is SP - CP = 5k - 4k = k. Profit percentage is (profit / CP) * 100 = (k / 4k) * 100 = 25%. The constant k cancels out, so any numbers proportional to 4 and 5 can be used. Step-by-Step Solution: Let CP = 4 units, SP = 5 units (simple representation of the ratio 4 : 5). Profit = SP - CP = 5 - 4 = 1 unit. Profit percentage = (profit / CP) * 100. Thus, profit% = (1 / 4) * 100. (1 / 4) * 100 = 25%. Verification / Alternative check: Use actual rupee values maintaining the ratio. For example, CP = Rs 400 and SP = Rs 500. Profit = 500 - 400 = Rs 100. Profit percentage = (100 / 400) * 100 = 25%. This again confirms that 25% is the correct profit percentage for the given ratio. Why Other Options Are Wrong: A profit of 27.5% or 15% or 10% would imply different CP : SP ratios. For instance, a 10% profit would correspond to CP : SP = 10 : 11, not 4 : 5. Hence those percentages do not match the given ratio 4 : 5. Common Pitfalls: Some learners invert the ratio and treat it as SP : CP, which would lead to a wrong calculation. Others attempt to convert the ratio directly into a percentage without using profit = SP - CP. Always express CP and SP in terms of the same variable and then compute profit percentage carefully. Final Answer: The profit percentage on the article is 25 percent.

Question 12

A fruit vendor buys 12 bananas for Rs 60 and later sells 5 bananas for Rs 32. What percentage gain does the vendor make on his overall transaction?

Accepted Answer

Introduction / Context: This is a basic profit and loss question involving unit cost and unit selling price. Such questions are very common in aptitude exams because they test whether a learner understands how to compare cost price and selling price when the items are sold in different group sizes. Here, a fruit vendor buys bananas in one batch and sells them in another, and we have to compute the percentage gain on the overall transaction. Given Data / Assumptions: - The vendor buys 12 bananas for Rs 60. - The vendor sells 5 bananas for Rs 32. - All bananas are assumed to be of equal quality and size. - We assume no wastage or leftover bananas. Concept / Approach: Profit or loss percentage is always calculated on cost price. First we find the cost price per banana, then the selling price per banana, and then compare them. The basic formulas used are: profit = selling price - cost price profit percent = (profit / cost price) * 100 When the number of items is the same, it is convenient to compare per unit prices. Step-by-Step Solution: Step 1: Cost price of 12 bananas = Rs 60. Step 2: Cost price per banana = 60 / 12 = Rs 5. Step 3: Selling price of 5 bananas = Rs 32. Step 4: Selling price per banana = 32 / 5 = Rs 6.4. Step 5: Profit per banana = 6.4 - 5 = Rs 1.4. Step 6: Profit percent = (1.4 / 5) * 100 = 28%. Verification / Alternative check: We can also consider a common multiple of bananas, for example 60 bananas. Cost price for 60 bananas = 60 * 5 = Rs 300. Selling price for 60 bananas = 60 * 6.4 = Rs 384. Profit = 384 - 300 = Rs 84. Profit percent = (84 / 300) * 100 = 28%. This confirms the earlier calculation. Why Other Options Are Wrong: Option 32 gives a higher gain than the correct value and would correspond to a larger selling price per banana than actually given. Option 24 underestimates the gain and would arise if someone used an incorrect cost base. Option 22 also understates the gain and could come from rounding or using 6.2 instead of 6.4 as selling price per banana. Common Pitfalls: A frequent mistake is to compare 60 and 32 directly without converting to per banana values. Another pitfall is to treat 60 and 32 as profit and cost, which is incorrect, or to divide by the wrong number of bananas. Learners should remember that profit percentage must always be compared to cost price, not selling price. Final Answer: The vendor makes a profit of 28% on the transaction.

Question 13

A bag is sold for Rs 230 at a profit of 15%. What would be the selling price of the same bag if the shopkeeper wants to earn a profit of 20% instead?

Accepted Answer

Introduction / Context: This profit and loss question checks the ability to back-calculate cost price from a known selling price and profit percentage, and then recalculate a new selling price for a different profit percentage. Such questions are standard in competitive exams and help students understand how profit percentages are applied in commercial situations. Given Data / Assumptions: - Selling price with 15% profit = Rs 230. - Required profit for the second case = 20%. - The cost price of the bag remains the same in both cases. - No additional costs or taxes are involved. Concept / Approach: We use the relation between cost price, selling price, and profit percent: selling price = cost price * (100 + profit percent) / 100 To find cost price from a known selling price and profit percent, we reverse the formula: cost price = selling price * 100 / (100 + profit percent) Once the cost price is known, we use it again to find the new selling price for the desired profit percentage. Step-by-Step Solution: Step 1: Let cost price be C. Step 2: With 15% profit, 230 = C * 115 / 100. Step 3: Therefore C = 230 * 100 / 115 = 200. Step 4: For 20% profit, new selling price S = C * 120 / 100. Step 5: So S = 200 * 1.2 = Rs 240. Verification / Alternative check: Check the profit in each case. When sold at Rs 230, profit = 230 - 200 = Rs 30, which is 30 / 200 * 100 = 15%. When sold at Rs 240, profit = 40, which is 40 / 200 * 100 = 20%. Both percentages match the question data, so the solution is consistent. Why Other Options Are Wrong: Option Rs.250 would give a profit of 50 on a cost of 200, which is 25%, not 20%. Option Rs.205 gives almost no profit above cost price. Option Rs.200 is exactly the cost price and corresponds to zero profit, so it cannot represent 20% profit. Common Pitfalls: A common mistake is to increase Rs 230 directly by 5% to move from 15% profit to 20% profit. Profit percentages are always based on cost price, so we must go back to cost price first. Another pitfall is to mix up cost price and selling price in the percentage formula, which gives an incorrect answer. Final Answer: The bag should be sold at Rs 240 to earn a profit of 20%.

Question 14

The marked price of a chair is 40% more than its cost price. If the chair is sold for Rs 520 after giving a discount of Rs 40 on the marked price, what is the profit percentage earned on the sale?

Accepted Answer

Introduction / Context: This problem combines the ideas of marked price, discount, and profit. Many real life shopkeeping situations involve marking goods above cost, then offering a discount, and still earning profit. The learner must be able to move from marked price back to cost price and then compare cost and selling price to compute profit percentage. Given Data / Assumptions: - Marked price is 40% more than cost price. - The final selling price is Rs 520. - A discount of Rs 40 is given on the marked price. - Only one item is considered, and there are no taxes or extra costs. Concept / Approach: We use these relations: marked price = cost price * 1.4 selling price = marked price - discount profit = selling price - cost price profit percent = (profit / cost price) * 100 First we find the marked price using the selling price and discount, then find the cost price, and finally compute the profit percentage. Step-by-Step Solution: Step 1: Selling price S = Rs 520. Step 2: Discount = Rs 40, so marked price M = S + discount = 520 + 40 = Rs 560. Step 3: Marked price is 40% above cost price, so M = 1.4 * cost price. Step 4: Therefore cost price C = 560 / 1.4 = Rs 400. Step 5: Profit = S - C = 520 - 400 = Rs 120. Step 6: Profit percent = 120 / 400 * 100 = 30%. Verification / Alternative check: We can also compute directly from cost price. If cost is Rs 400, then 40% of 400 is 160, so marked price should be 560. After allowing a flat discount of 40, we again reach 520 as selling price. The profit of 120 on a cost of 400 is clearly 30%, so the result is confirmed by two consistent checks. Why Other Options Are Wrong: Option 33 would require a profit of about Rs 132, which does not match the given numbers. Option 40 would be correct only if the selling price were higher for the same cost. Option 25 comes from mixing up marked price and cost price or using 520 as the base in the denominator, which is incorrect for profit percentage. Common Pitfalls: Learners sometimes treat marked price as cost price or calculate profit on marked price instead of on cost price. Another common error is forgetting that discount reduces marked price, not cost price. Careful identification of each price level avoids these mistakes. Final Answer: The profit percentage earned on the sale of the chair is 30%.

Question 15

The selling price of a watch is Rs 966 and the profit percentage on this sale is 15%. If the same watch is sold for Rs 798 instead, what will be the percentage loss on this second sale?

Accepted Answer

Introduction / Context: This question mixes both profit and loss on the same article but at two different selling prices. It tests knowledge of how to find the cost price from a given profit situation and then use that cost price to compute a loss in another situation. Such questions often appear in bank and management entrance examinations. Given Data / Assumptions: - Selling price for the first sale = Rs 966 with 15% profit. - Selling price for the second sale = Rs 798. - The cost price of the watch is the same in both cases. - No additional charges, tax, or discount are involved in the prices listed. Concept / Approach: We again use the core formulas of profit and loss: selling price = cost price * (100 + profit percent) / 100 cost price = selling price * 100 / (100 + profit percent) loss = cost price - selling price loss percent = (loss / cost price) * 100 The key is to calculate cost price from the first scenario and then calculate loss percentage in the second scenario. Step-by-Step Solution: Step 1: Let cost price be C. Step 2: For 15% profit, 966 = C * 115 / 100. Step 3: So C = 966 * 100 / 115 = 840. Step 4: In the second sale, selling price S2 = Rs 798. Step 5: Loss = C - S2 = 840 - 798 = Rs 42. Step 6: Loss percent = 42 / 840 * 100 = 5%. Verification / Alternative check: We can cross check by finding what 5% of 840 is. Five percent of 840 is 840 * 5 / 100 = Rs 42, which exactly matches the loss. Also, selling price after a 5% loss should be 95% of cost, that is 840 * 95 / 100 = 798, which agrees with the second selling price. Hence the result is confirmed. Why Other Options Are Wrong: Option 8 corresponds to a larger loss than actually occurs and would give a selling price much smaller than 798. Options 7.21 and 6.26 are approximate values that might arise from rounding at intermediate steps or using 966 instead of cost price as the base, but they do not match the correct method where cost price is the reference. Common Pitfalls: Learners often try to compare 966 and 798 directly and compute a percentage on that difference, which is incorrect because profit or loss percentage is always calculated on cost price, not on the higher selling price. Another pitfall is forgetting to convert percentage gains to multipliers correctly when going from selling price back to cost price. Final Answer: The loss on selling the watch for Rs 798 is 5%.

Question 16

A and B invest Rs 3000 and Rs 2400 respectively in a business. After one year, the business makes a total loss of Rs 720. Assuming that loss is shared in proportion to their investments, how much loss will B bear?

Accepted Answer

Introduction / Context: This is a partnership and loss distribution question. In business partnerships, both profits and losses are usually shared in the ratio of the investments made by each partner, provided there is no separate agreement about sharing. Here we need to determine B's share of the total loss based on the ratio of amounts invested by A and B. Given Data / Assumptions: - A invests Rs 3000. - B invests Rs 2400. - Total loss after one year = Rs 720. - Loss is assumed to be shared in the ratio of their investments. Concept / Approach: When no special conditions are mentioned, the share of each partner in profit or loss is proportional to the amount invested and the time period for which it is invested. Here time is the same for both, so we only use the investment amounts. We find the ratio of investments, then apply that ratio to the total loss to get each partner's share. Step-by-Step Solution: Step 1: Investment by A = 3000, by B = 2400. Step 2: Ratio of investments = 3000 : 2400. Step 3: Divide both terms by 600 to simplify: 3000 / 600 = 5, 2400 / 600 = 4, so ratio = 5 : 4. Step 4: Total parts in this ratio = 5 + 4 = 9. Step 5: Total loss = Rs 720, so one part = 720 / 9 = Rs 80. Step 6: B's share of loss = 4 parts = 4 * 80 = Rs 320. Verification / Alternative check: Check that A's share of loss is 5 * 80 = Rs 400. Then A's loss plus B's loss = 400 + 320 = 720, which matches the total loss. Also note that A's share is larger because he invested more, which matches the logical expectation. Why Other Options Are Wrong: Option Rs. 72 is far too low and would not add up correctly to the total loss when combined with A's share. Option Rs. 400 matches A's share, not B's, so it is incorrect for the question asked. Option Rs. 360 corresponds to a wrong distribution ratio and would imply an incorrect investment ratio. Common Pitfalls: A typical mistake is to divide the total loss equally between A and B, ignoring the investment ratio. Another error is to invert the ratio or to forget to simplify the ratio correctly before applying it. Always compute the ratio first, find the sum of ratio parts, and then allocate the profit or loss. Final Answer: B will bear a loss of Rs 320.

Question 17

A merchant buys 25 litres of milk every day at Rs 12 per litre. He then mixes 5 litres of water, which is free, and sells the entire 30 litre mixture at Rs 10.40 per litre. What is his overall gain or loss percentage on this transaction?

Accepted Answer

Introduction / Context: This question involves a classic case of mixing water with milk to increase profit. Milk is purchased at a cost, water is free, and the mixture is sold at a single uniform rate. The trick is that although the selling price per litre may be lower than the buying price per litre, the addition of free water can still produce an overall profit. Given Data / Assumptions: - Milk bought = 25 litres at Rs 12 per litre. - Water mixed = 5 litres, cost assumed to be zero. - Total mixture = 30 litres. - Selling price of mixture = Rs 10.40 per litre. - No wastage occurs and the entire mixture is sold. Concept / Approach: We first compute the total cost price of the mixture, which is simply the cost of milk since water is free. Then we compute the total selling price by multiplying the mixture quantity by the selling price per litre. Finally, we compare total selling price with total cost price to obtain profit and profit percentage. Step-by-Step Solution: Step 1: Cost of 25 litres of milk = 25 * 12 = Rs 300. Step 2: Water is free, so total cost price C = Rs 300. Step 3: Total quantity after mixing = 25 + 5 = 30 litres. Step 4: Total selling price S = 30 * 10.40 = Rs 312. Step 5: Profit = S - C = 312 - 300 = Rs 12. Step 6: Profit percent = (12 / 300) * 100 = 4%. Verification / Alternative check: We can compute effective selling price per litre in terms of cost. Total cost is 300 for 30 litres, which means effective cost per litre of mixture is 300 / 30 = Rs 10. The merchant actually charges Rs 10.40 per litre, which is 0.40 more than effective cost. Extra 0.40 on base 10 is 4%, confirming the profit percentage is 4% on cost price. Why Other Options Are Wrong: Option 8% profit would require a profit double of what is actually earned. Option 2% profit and 6% profit correspond to total selling prices that do not match the given rate of Rs 10.40 per litre when applied to 30 litres. Only 4% keeps both cost and given selling price consistent. Common Pitfalls: One common mistake is to compare 12 and 10.40 directly and assume a loss because the selling price per litre appears less than the purchase price per litre. This ignores the effect of free water. Another error is to forget to multiply by the total number of litres when computing total selling price. Always work with totals when mixture is involved. Final Answer: The merchant makes a 4% profit on the transaction.

Question 18

A retailer receives a 40% discount on the printed price (marked price) of an article and then sells the article at the full printed price. What is the retailer's gain percentage on this transaction?

Accepted Answer

Introduction / Context: This question deals with the concept of trade discount and profit. The retailer buys goods from a wholesaler at a discount on the marked price and then sells them to customers at the full marked price, thereby earning a profit. The task is to determine this profit percentage based on the discount percentage. Given Data / Assumptions: - Printed (marked) price of the article is P. - Retailer gets 40% discount on P. - Retailer sells at the full printed price P. - No other expenses like tax or transport are considered. Concept / Approach: We treat the marked price as a base to find cost price and selling price. If the discount is 40%, the retailer pays only 60% of the marked price. Then he sells at 100% of the marked price. Profit percentage is calculated on cost price. The formulas used are: cost price = marked price * (100 - discount percent) / 100 profit = selling price - cost price profit percent = (profit / cost price) * 100 Step-by-Step Solution: Step 1: Let marked price P = 100 units for easy calculation. Step 2: Discount is 40%, so cost price for retailer C = 100 - 40 = 60. Step 3: Selling price S = full marked price = 100. Step 4: Profit = S - C = 100 - 60 = 40. Step 5: Profit percent = (40 / 60) * 100 = 66.666..., which is 66 2/3%. Verification / Alternative check: If we work with an actual marked price, say Rs 300, cost to retailer would be 60% of 300 = Rs 180. Selling price remains Rs 300. Profit = 120. Profit percent = 120 / 180 * 100 = 66.666..., again confirming 66 2/3%. Since percentage calculations scale linearly, any chosen marked price gives the same profit percent. Why Other Options Are Wrong: Option 40 would be correct only if cost price were 100 and selling price were 140, which is not the situation here. Option 55 and 75 do not satisfy the relation of a 40% discount on marked price followed by sale at marked price when checked algebraically. Only 66 2/3% satisfies the conditions given in the problem. Common Pitfalls: A frequent error is to subtract the discount from selling price and think that the remaining percentage is profit. Another pitfall is to compute profit percentage on the marked price instead of on cost price. Always calculate profit percentage as profit divided by cost price, multiplied by 100. Final Answer: The retailer's gain percentage is 66 2/3%.

Question 19

If the cost price of 25 pens is equal to the selling price of 20 pens, what is the profit percentage made when each pen is sold at this selling price?

Accepted Answer

Introduction / Context: This is a standard profit percentage question where cost price and selling price are related through numbers of items rather than direct rupee values. It tests the idea that when the total cost of a certain number of items equals the total selling price of a smaller number of items, there is a profit in selling each item at that rate. Given Data / Assumptions: - Cost price of 25 pens is equal to selling price of 20 pens. - All pens are identical and sold at the same selling price per pen. - No additional costs such as packaging are involved. Concept / Approach: Let cost price per pen be C and selling price per pen be S. The equation from the question is: 25 * C = 20 * S From this, we can express S in terms of C and then use the profit percentage formula: profit = S - C profit percent = (profit / C) * 100 Step-by-Step Solution: Step 1: Let cost price per pen = C and selling price per pen = S. Step 2: Given 25C = 20S. Step 3: So S = 25C / 20 = (5/4) * C = 1.25C. Step 4: Profit per pen = S - C = 1.25C - C = 0.25C. Step 5: Profit percent = (0.25C / C) * 100 = 25%. Verification / Alternative check: Assume a convenient cost price per pen, say C = Rs 4. Then cost price of 25 pens = 25 * 4 = Rs 100. This must equal the selling price of 20 pens, so S = 100 / 20 = Rs 5 per pen. Profit per pen = 5 - 4 = Rs 1. Profit percent = 1 / 4 * 100 = 25%, confirming the calculation. Why Other Options Are Wrong: Option 20% would correspond to a selling price of 1.2C, which does not satisfy 25C = 20S. Option 15% and 5% represent even smaller markups and clearly cannot produce equality between 25C and 20S. Only 25% matches the relationship given in the problem. Common Pitfalls: Students sometimes reverse the ratio and assume 20C = 25S or incorrectly treat the numbers of pens as the percentage directly. It is important to set up the equation carefully and then isolate S in terms of C before applying the profit percentage formula. Final Answer: The profit made on each pen is 25% of the cost price.

Question 20

A loss of 20% calculated on the selling price of an article is equal to a loss of x% calculated on its cost price. What is the value of x?

Accepted Answer

Introduction / Context: This question explores the difference between calculating percentage loss on selling price and on cost price. The same absolute loss amount can represent different percentages depending on which base value is used. It is a slightly conceptual profit and loss question that requires algebraic manipulation and understanding of definitions. Given Data / Assumptions: - Loss is 20% of the selling price. - The same loss is x% of the cost price. - We assume one single article with cost price C and selling price S. - Loss is positive and both prices are greater than zero. Concept / Approach: Let cost price be C and selling price be S. Loss = C - S. Given that this loss is 20% of selling price, we have: C - S = 0.20 * S We also know that the same loss equals x% of cost price: C - S = (x / 100) * C We solve these equations to express x in terms of known constants. The key idea is to first find the relationship between C and S and then compute x from that relationship. Step-by-Step Solution: Step 1: From C - S = 0.20S, we get C = S + 0.20S = 1.20S. Step 2: Therefore S = C / 1.20. Step 3: Loss L = C - S = C - C / 1.20. Step 4: L = C * (1 - 1 / 1.20) = C * (1 - 0.8333...) = C * 0.1666..., which is C / 6. Step 5: Since L = (x / 100) * C, we have C / 6 = (x / 100) * C. Step 6: Cancel C on both sides to get 1 / 6 = x / 100, so x = 100 / 6 = 16.666..., which is 16 2/3%. Verification / Alternative check: Take an example. Let selling price S = Rs 120. Then loss is 20% of 120, that is Rs 24. So cost price C = S + loss = 120 + 24 = Rs 144. Now loss as a percentage of cost price is 24 / 144 * 100 = 16.666..., which is 16 2/3%. This matches our algebraic solution. Why Other Options Are Wrong: Option 20% repeats the given percentage on selling price, not on cost price, and does not satisfy the equations. Option 20 with no percent sign is incomplete. Option 16 understates the loss relative to cost price and would not give equal loss amounts in both definitions. Common Pitfalls: Many students incorrectly assume that the same percentage applies to both cost price and selling price, which is not true. Another mistake is to treat x as 20 directly without doing the algebra. Always derive the relationship between cost price and selling price when the loss is given as a fraction of one of them. Final Answer: The required value of x is 16 2/3%.

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