Question 1

A sold an article to B at 40% profit and B sold it to C at 50% profit, then what will be profit percent with respect to A ?

Accepted Answer

% Profit with respect to A = 40 + 50 + (40 x 50)/100 = 90 + 20 = 110 %.

Question 2

If a trader sold two cars each at Rs. 404415 and gains 15% on the first and loses 15% on the second, then his profit or loss percent on the whole is ?

Accepted Answer

SP of each car is Rs. 404415, he gains 15% on first car and losses 15% on second car. In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100 = (15)(15)/100 % = 2.25%

Question 3

If the cost price of an article is 75% of its selling price, then by how many percent does the selling price exceed the cost price, that is, what is the profit percentage on the cost price?

Accepted Answer

Introduction / Context: This question is about the relationship between cost price and selling price when one is given as a percentage of the other. It checks if you can correctly convert a statement like “cost price is 75% of selling price” into a profit percentage. Such problems are very common in profit and loss chapters and they test whether you understand which quantity is the base for the percentage being described. Careful algebra quickly leads to the correct profit percentage without confusion. Given Data / Assumptions: - Cost price (CP) is 75% of selling price (SP). - That means CP = 0.75 * SP. - We must find the profit percentage on the cost price. - All values are conceptual; no actual rupee amount is needed. Concept / Approach: Profit percentage is always calculated using cost price as the base: Profit% = (Profit / CP) * 100, where Profit = SP - CP. The statement CP = 75% of SP can be rewritten in algebraic form and used to express SP and CP in terms of a convenient variable. Typically, we assume a simple numerical value for SP (for example, Rs. 100) to simplify the arithmetic. Once we have CP and SP in that form, profit and profit percentage become straightforward to compute. This approach is particularly useful for mental math in exams. Step-by-Step Solution: Let selling price (SP) be Rs. 100 for convenience. Given that cost price is 75% of selling price, CP = 75% of 100 = Rs. 75. Profit = SP - CP = 100 - 75 = Rs. 25. Profit percentage is calculated on CP: Profit% = (Profit / CP) * 100. So, Profit% = (25 / 75) * 100. Compute 25 / 75 = 1 / 3. Thus, Profit% = (1 / 3) * 100 ≈ 33.33%. Verification / Alternative check: We can work symbolically: Let SP = S, then CP = 0.75S. Profit = S - 0.75S = 0.25S. Profit% = (0.25S / 0.75S) * 100 = (0.25 / 0.75) * 100. Simplify 0.25 / 0.75 = 1 / 3, so profit% = (1 / 3) * 100 ≈ 33.33%. This symbolic method perfectly matches the earlier numeric approach. Why Other Options Are Wrong: - 23.47% and 25% are lower than the correct value; they arise from incorrect division or using selling price as the base. - 20% assumes a smaller difference between SP and CP than actually exists in the given relationship. - 30% is close but still incorrect; it results from approximate mental math that ignores exact fractions. Common Pitfalls: A common mistake is to treat 75% as the profit percentage instead of a relationship between CP and SP. Another error is to calculate profit percentage using selling price as the base, giving (25 / 100) * 100 = 25%, which is incorrect. Students sometimes forget that profit is always calculated relative to cost price, not relative to selling price. Final Answer: The selling price exceeds the cost price by a profit of approximately 33.33%.

Question 4

A shopkeeper gives a 20% discount on the marked price of a pair of books. In addition, for every 9 pairs of books that a customer pays for, the shopkeeper gives 1 more pair of books free. If on this combined offer he still earns an overall profit of…

Accepted Answer

Introduction / Context: This question combines two common commercial practices: percentage discount on marked price and giving free units as part of a promotional offer. Despite these apparent reductions, the shopkeeper still manages to earn a profit. The problem asks us to determine how much the marked price is increased above the cost price to sustain a 26% overall profit under these conditions. Such questions are designed to test multi-step reasoning with discount, free goods, and profit percentage all in one scenario, which is typical of competitive exams on quantitative aptitude. Given Data / Assumptions: - Discount on marked price = 20%. - For every 9 pairs of books purchased, 1 extra pair is given free, so the customer receives 10 pairs but pays for only 9. - Overall profit on the entire transaction = 26% on cost price. - All pairs of books are identical and have the same cost price and marked price. - We must find the percentage by which marked price exceeds cost price. Concept / Approach: Let the cost price per pair of books be C and the marked price per pair be M. Because of the 20% discount, the effective selling price per paid pair is 0.8M. When a customer buys 9 pairs, he pays for 9 pairs but receives 10 pairs (9 paid + 1 free). The shopkeeper's total revenue for those 10 pairs is 9 * 0.8M = 7.2M, while his total cost is 10C. The overall profit percentage is (Revenue - Cost) / Cost * 100, which is given as 26%. Using this relationship we can form an equation involving M and C and solve for M in terms of C to obtain the markup percentage on cost price. Step-by-Step Solution: Let cost price of one pair of books = C rupees. Let marked price of one pair of books = M rupees. Discount on marked price = 20%, so selling price per paid pair = 0.80M. In the offer, customer pays for 9 pairs and gets 10 pairs (1 pair free). Total revenue for 10 pairs = 9 * 0.80M = 7.2M. Total cost for 10 pairs = 10C. Profit = Revenue - Cost = 7.2M - 10C. Given overall profit% = 26%, so (7.2M - 10C) / (10C) * 100 = 26. So, (7.2M - 10C) / 10C = 0.26. Therefore, 7.2M - 10C = 2.6C, because 0.26 * 10C = 2.6C. So, 7.2M = 12.6C. Thus, M = 12.6C / 7.2 = 1.75C. Marked price is therefore 1.75 times the cost price, i.e., a 75% markup. Verification / Alternative check: If C = Rs. 100, then M = 1.75 * 100 = Rs. 175. Selling price per paid pair after 20% discount = 0.80 * 175 = Rs. 140. For 9 paid pairs, revenue = 9 * 140 = Rs. 1,260. Cost of 10 pairs = 10 * 100 = Rs. 1,000. Profit = 1,260 - 1,000 = Rs. 260. Profit% = 260 / 1,000 * 100 = 26%, which matches the given data. Why Other Options Are Wrong: - 35%, 65%, and 50% are lower markups and would not generate enough profit to reach 26% after discount and free goods. - 26% is the overall profit percentage, not the markup on the marked price; equating them would be a conceptual mistake. - Only a 75% markup on cost price is consistent with a 20% discount plus the 9 + 1 free scheme and 26% overall profit. Common Pitfalls: A common misunderstanding is to treat the 26% profit directly as the difference between cost price and marked price without accounting for the discount and free pair. Some students ignore the free pair entirely, effectively assuming revenue is for 9 pairs but cost is also for 9 pairs, which is incorrect. Another pitfall is computing profit percentage on marked price rather than on cost price, which changes the base and leads to wrong answers. Final Answer: The marked price is 75% higher than the cost price.

Question 5

Mohan purchases 13 identical articles for Rs. 12 in total and then sells all of them at the rate of 12 articles for Rs. 13. Based on this buying and selling pattern, what is his percentage profit on the cost price?

Accepted Answer

Introduction / Context: This is a typical profit and loss question where the trader buys and sells items in unequal number-price combinations, such as “13 for Rs. 12” and “12 for Rs. 13”. These are very common patterns in competitive exams because they test conceptual understanding of unit cost price and unit selling price. The overall profit percentage is found by comparing the cost price per article with the selling price per article. Careful handling of fractions is important to avoid calculation errors and to get the exact profit percentage. Given Data / Assumptions: - Mohan buys 13 articles for Rs. 12 (this is the total cost for 13 units). - He sells the articles at the rate of 12 articles for Rs. 13. - All articles are identical with the same cost price and selling price per article. - We must find his profit percentage on the cost price. Concept / Approach: To find the profit percentage, we first determine the cost price per article and the selling price per article. Cost price per article is simply total cost divided by number of articles bought in that lot. Similarly, selling price per article is total selling amount divided by the number of articles sold in that selling lot. Once we know CP per unit and SP per unit, we calculate profit per unit as SP - CP and then compute Profit% = (Profit per unit / CP per unit) * 100. Since all articles behave identically, using just one article is enough to understand the entire transaction pattern. Step-by-Step Solution: Total cost of 13 articles = Rs. 12. Cost price (CP) per article = 12 / 13 rupees. He sells at 12 articles for Rs. 13. Selling price (SP) per article = 13 / 12 rupees. Profit per article = SP - CP = (13 / 12) - (12 / 13). Compute the difference: (13 / 12) - (12 / 13) = (169 / 156) - (144 / 156) = 25 / 156. Profit per article = 25 / 156 rupees. Profit percentage = (Profit per article / CP per article) * 100. So, Profit% = (25 / 156) / (12 / 13) * 100. Simplify: (25 / 156) * (13 / 12) * 100 = (25 * 13 * 100) / (156 * 12). Compute: 25 * 13 = 325; 156 * 12 = 1,872. Thus Profit% = (325 * 100) / 1,872 ≈ 17.36%. Verification / Alternative check: Assume Mohan buys 156 articles in bulk, which is the least common multiple of 12 and 13. For every 13 articles, he pays Rs. 12, so for 156 articles he has 156 / 13 = 12 lots and pays 12 * 12 = Rs. 144. He sells at 12 for Rs. 13, so number of lots for 156 articles is 156 / 12 = 13 lots, and revenue = 13 * 13 = Rs. 169. Profit = 169 - 144 = Rs. 25 on cost price 144, so Profit% = 25 / 144 * 100 ≈ 17.36%, matching the earlier calculation. Why Other Options Are Wrong: - 19.47% and 12.5% do not match the correct fraction and arise from approximate or mistaken arithmetic. - 11.11% is a common distractor based on confusion with 9-for-10 or similar patterns. - 15% is a rounded guess and not supported by accurate fraction-based computation. Common Pitfalls: Students sometimes incorrectly compare 13 and 12 directly and think profit is simply 1 rupee on 12 rupees, giving 8.33%, which ignores the number of articles. Another mistake is to compute profit percentage based on total selling price or total buying price without normalizing to units. Neglecting to use a convenient common multiple (like 156) can make the arithmetic look harder than it really is. Final Answer: Mohan earns a profit of approximately 17.36% on his cost price.

Question 6

A trader marks his goods so that after allowing a discount of 10% on the marked price he still gains a profit of 15% on his cost price. If an article costs him Rs. 720, what should be the marked price of the article?

Accepted Answer

Introduction / Context: This question is about determining the marked price of an article when the shopkeeper wants to allow a fixed discount yet still achieve a desired profit. This reflects a very common real-life pricing strategy in retail stores. In competitive exams, such questions test the ability to combine discount and profit percentage concepts correctly. The method involves first calculating the required selling price for the target profit and then relating that selling price to the marked price through the given discount percentage. Given Data / Assumptions: - Cost price (CP) of the article = Rs. 720. - Desired profit percentage = 15% on CP. - Discount on marked price = 10%. - We must find the marked price (MP) of the article. Concept / Approach: First we compute the selling price that would give a 15% profit on the cost price using SP = CP * (1 + profit%). After that, we know that this selling price is obtained after giving a 10% discount on the marked price, meaning SP = MP * (1 - discount%). Therefore we can set up the equation MP * 0.90 = required SP and solve for MP. This two-step approach ensures we correctly handle both the desired profit and the offered discount. Step-by-Step Solution: Given CP = Rs. 720 and desired profit% = 15%. Required selling price (SP) = CP * (1 + 15/100) = 720 * 1.15. Compute SP: 720 * 1.15 = 720 * (115 / 100) = 828. So, SP must be Rs. 828 to obtain 15% profit. Next, discount on the marked price is 10%, so SP = MP * (1 - 10/100) = MP * 0.90. Thus, 0.90 * MP = 828. MP = 828 / 0.90 = 828 * (10 / 9) = 920. Therefore, the marked price must be Rs. 920. Verification / Alternative check: Check discount: 10% of 920 = 0.10 * 920 = 92, so discounted price = 920 - 92 = Rs. 828. Check profit on CP: Profit = 828 - 720 = Rs. 108. Profit% = 108 / 720 * 100 = 15%, exactly as required. Both checks confirm that MP = Rs. 920 is correct. Why Other Options Are Wrong: - Rs. 900 and Rs. 880 give lower selling prices after a 10% discount, which lead to profit percentages lower than 15%. - Rs. 820 is even smaller; after a 10% discount, SP would be 738, which is only a 2.5% profit on 720. - Rs. 950 would yield a higher profit percentage than 15%, exceeding the target. Common Pitfalls: Students sometimes treat the 10% discount as being applied on cost price rather than on marked price, which is conceptually incorrect. Another mistake is to try to apply profit and discount directly on the same base without separating the two steps. Forgetting to convert percentages into decimal multipliers, like 1.15 and 0.90, can also create algebraic confusion. Final Answer: The marked price of the article should be Rs. 920.

Question 7

Savita sold an item for Rs. 6,500 and incurred a loss of 20% on its cost price. At what price should she have sold the same item in order to earn a profit of 20% instead?

Accepted Answer

Introduction / Context: This profit and loss question involves two different selling prices for the same item, one resulting in a loss and the other intended to result in a profit. The cost price remains the same in both scenarios, so once we determine the cost price from the loss situation, it can be used directly to find the selling price corresponding to the desired profit. This pattern is very common in aptitude exams and is a good example of how one scenario can be used to derive missing information in another scenario. Given Data / Assumptions: - First selling price (SP1) = Rs. 6,500. - At SP1, Savita incurs a loss of 20% on the cost price. - Second selling price (SP2) should give a profit of 20% on the same cost price. - We must find SP2. Concept / Approach: In the loss situation, the relationship is SP1 = CP * (1 - loss%), where loss% = 20%. From this we can compute the cost price CP. In the profit situation, the relationship is SP2 = CP * (1 + profit%), again with profit% = 20%. Both percentages are applied to the same cost price, so after calculating CP once, we can directly use it to calculate the second selling price. This strategy neatly links the loss case and the profit case through a single CP value. Step-by-Step Solution: In the first case, loss = 20%, so SP1 = CP * (1 - 0.20) = CP * 0.80. Given SP1 = Rs. 6,500, so 6,500 = 0.80 * CP. Thus, CP = 6,500 / 0.80. Compute CP: 6,500 / 0.80 = 6,500 * (10 / 8) = 6,500 * (5 / 4) = 8,125. Therefore, cost price CP = Rs. 8,125. Now, for a profit of 20%, SP2 = CP * (1 + 0.20) = CP * 1.20. So SP2 = 8,125 * 1.20. Compute SP2: 8,125 * 1.20 = 8,125 * (6 / 5) = 9,750. Therefore, she should have sold the item for Rs. 9,750 to earn a profit of 20%. Verification / Alternative check: Check loss scenario: 20% of 8,125 = 0.20 * 8,125 = 1,625; SP1 = 8,125 - 1,625 = 6,500, which matches the given selling price with a 20% loss. Check profit scenario: 20% of 8,125 = 1,625; SP2 = 8,125 + 1,625 = 9,750, matching our computed SP2. Both checks confirm that CP and SP2 are consistent with the required conditions. Why Other Options Are Wrong: - Rs. 10,375 would correspond to a profit greater than 20% on the cost price. - Rs. 8,125 is the cost price itself, which would imply zero profit or loss, not 20% profit. - Rs. 9,000 gives a profit percentage less than 20%. - “Cannot be determined” is incorrect because enough information is given to uniquely determine CP and then SP2. Common Pitfalls: Some students mistakenly average the two selling prices or treat the 20% loss and 20% profit as cancelling each other, which is wrong. Another error is to calculate the profit percentage based on the lower selling price rather than the cost price. Forgetting to multiply properly by the fractional form 6/5 when going from CP to SP2 is also a common arithmetic slip. Final Answer: She should have sold the item for Rs. 9,750 to earn a 20% profit.

Question 8

A bread seller X marks the price of each bread packet 150% above its cost price and usually allows a discount of 40% on the marked price, making a profit of Rs. 30 on each packet. If instead X allows a discount of 37.5% on the marked price, what tot…

Accepted Answer

Introduction / Context: This problem combines markup, discount, and absolute profit per unit in a single scenario. First, the bread seller marks his goods 150% above cost, then offers various discount percentages on this marked price. The question asks for the resulting total profit when the discount rate is changed but the cost price and marked price structure remain the same. Such questions are typical in profit and loss topics and test the ability to move between absolute rupee profit and percentage-based pricing strategies in a clear, stepwise manner. Given Data / Assumptions: - Let cost price per bread packet be C rupees. - Marked price (MP) is 150% above cost price, so MP = C * (1 + 1.5) = 2.5C. - With a 40% discount on MP, profit per packet is Rs. 30. - Later, discount is changed to 37.5% on MP. - We must find the total profit on 80 packets at the 37.5% discount rate. Concept / Approach: First we use the initial situation (40% discount, Rs. 30 profit) to determine the actual cost price C and marked price MP. Under a 40% discount, the selling price SP1 is 60% of MP (because 100% - 40% = 60%). The profit per packet in this situation is SP1 - C, which is given as Rs. 30. This gives us an equation in terms of C that we can solve. Once we know C and MP, we consider the second scenario with a 37.5% discount, compute the new selling price per packet, find the new profit per packet, and then multiply by 80 packets to get total profit. Step-by-Step Solution: Marked price MP = 2.5C (since markup is 150% on cost). With a 40% discount, selling price SP1 = 60% of MP = 0.60 * 2.5C = 1.5C. Profit per packet in this case = SP1 - C = 1.5C - C = 0.5C. Given that this profit is Rs. 30, we have 0.5C = 30. So, C = 30 / 0.5 = 60 rupees. Therefore, MP = 2.5 * 60 = Rs. 150. Now consider the discount of 37.5%: new selling price SP2 = (100% - 37.5%) of MP = 62.5% of MP. So, SP2 = 0.625 * 150 = Rs. 93.75. New profit per packet = SP2 - C = 93.75 - 60 = Rs. 33.75. For 80 packets, total profit = 33.75 * 80 = Rs. 2,700. Verification / Alternative check: Recheck cost price and first scenario: MP = Rs. 150, 40% discount gives SP1 = 90, which would be a profit of 30 over C = 60. This matches the given condition. Recheck second scenario: 37.5% of 150 is 56.25, so discount amount = 56.25 and SP2 = 150 - 56.25 = 93.75. Profit per packet is 93.75 - 60 = 33.75, and 33.75 * 80 = 2,700, verifying our answer. Why Other Options Are Wrong: - Rs. 2,500 and Rs. 2,750 assume incorrect values for either cost price or new profit per packet. - Rs. 3,000 and Rs. 3,200 are too high and do not match the computed profit per packet. - Only Rs. 2,700 is consistent with both the given initial profit and the new discount rate. Common Pitfalls: Some students mistakenly apply the discount directly on cost price instead of marked price, which leads to a wrong value of cost price. Another frequent mistake is to add or subtract percentage values incorrectly instead of calculating actual rupee amounts for each step. Rounding off intermediate values too early, especially with decimals like 93.75, can create slight errors in the final profit figure. Final Answer: When offering a 37.5% discount, X earns a total profit of Rs. 2,700 on 80 bread packets.

Question 9

Raghunandan sells a machine for Rs. 45 lakh at a loss. If instead he had sold the machine for Rs. 55 lakh, his gain would have been nine times the amount of his original loss. What is the cost price of the machine in lakhs of rupees?

Accepted Answer

Introduction / Context: This problem involves two hypothetical selling prices of the same machine: one resulting in a loss and the other in a gain. What makes the question interesting is that the gain in the second scenario is specified as nine times the loss in the first scenario. Such questions are common in aptitude exams because they require you to form and solve a linear equation based on profit and loss relationships. The cost price remains the central unknown that connects both cases and is determined using the condition given about the relative sizes of loss and gain. Given Data / Assumptions: - In the first scenario, machine is sold for SP1 = Rs. 45 lakh at a loss. - In the second scenario, it would be sold for SP2 = Rs. 55 lakh at a gain. - The gain in the second scenario would be 9 times the loss in the first scenario. - The cost price (CP) of the machine is the same in both cases and is to be found. Concept / Approach: Let CP denote the cost price in lakhs. In the first case, loss = CP - 45 (because CP is greater than 45). In the second case, gain = 55 - CP (because CP is less than 55 there). The condition says that gain in the second case is nine times the loss in the first case: 55 - CP = 9 * (CP - 45). This is a simple linear equation in CP, which we can expand and solve. Once CP is known, we can verify that it indeed produces the stated relationship between loss and gain. Step-by-Step Solution: Let CP = x lakhs. First scenario: Sold at Rs. 45 lakh, so loss = x - 45 (since x > 45). Second scenario: Sold at Rs. 55 lakh, so gain = 55 - x. Given: gain in second case = 9 * loss in first case. Therefore, 55 - x = 9 * (x - 45). Expand the right-hand side: 55 - x = 9x - 405. Bring all terms to one side: 55 + 405 = 9x + x. So, 460 = 10x. Hence, x = 460 / 10 = 46. Therefore, CP = Rs. 46 lakh. Verification / Alternative check: Loss at SP1 = CP - SP1 = 46 - 45 = Rs. 1 lakh. Gain at SP2 = SP2 - CP = 55 - 46 = Rs. 9 lakh. The condition says gain is nine times the loss: 9 lakh = 9 * 1 lakh, which is true. Therefore, CP = 46 lakh perfectly satisfies the given condition. Why Other Options Are Wrong: - If CP were 54 lakh, the loss at 45 lakh would be 9 lakh and gain at 55 lakh would be 1 lakh, reversing the required ratio. - CP = 60 lakh or CP = 38 lakh would produce either only loss or only gain in both cases, which contradicts the question statement. - CP = 50 lakh fails the equation 55 - CP = 9(CP - 45) and does not give the gain as nine times the loss. Common Pitfalls: Mistaking which part is loss and which is gain can lead to reversing the equation and an incorrect answer. Another frequent error is setting 55 - CP = 9 * (45 - CP) instead of 9 * (CP - 45), which changes the sign of the loss. Some students try to average 45 and 55 directly, which ignores the crucial condition involving the ratio between gain and loss. Final Answer: The cost price of the machine is Rs. 46 lakhs.

Question 10

Two items A and B have equal cost prices. Item A is sold at a profit of 40%, and item B is sold at a price that is 20% less than the selling price of item A. If the total profit on both items together is Rs. 156, what is the cost price of item A?

Accepted Answer

Introduction / Context: This question deals with two items that share the same cost price but are sold under different conditions. The first item is sold at a 40% profit and the second item at a reduced selling price, 20% less than the first item's selling price. The combined profit in rupees is given, and from that we must deduce the common cost price. This type of question is common in competitive exams as it involves combining profit percentage, absolute profit, and relationships between different selling prices in a multi-step calculation. Given Data / Assumptions: - Cost price of item A = cost price of item B = C rupees. - Item A is sold at a profit of 40% on its cost price. - Selling price of item B is 20% less than the selling price of item A. - Total profit on both items together is Rs. 156. - We must find the value of C, the cost price of item A. Concept / Approach: First, express the selling price of item A in terms of C using the 40% profit: SP_A = 1.40C. Then, because item B is sold at 20% less than this selling price, SP_B = SP_A * (1 - 0.20) = 0.80 * SP_A. Substituting SP_A, this gives SP_B in terms of C. Once both selling prices are expressed in terms of C, we can compute total selling price and total cost price, and use the given absolute profit of Rs. 156 to form an equation. Solving this equation for C gives the common cost price of both items. Step-by-Step Solution: Let the cost price of each item (A and B) be C rupees. Item A is sold at 40% profit, so SP_A = C * (1 + 0.40) = 1.40C. The selling price of item B is 20% less than SP_A. So, SP_B = SP_A * (1 - 0.20) = 1.40C * 0.80 = 1.12C. Total cost price of both items = C + C = 2C. Total selling price = SP_A + SP_B = 1.40C + 1.12C = 2.52C. Total profit = Total SP - Total CP = 2.52C - 2C = 0.52C. We are given that total profit = Rs. 156, so 0.52C = 156. Thus, C = 156 / 0.52. Compute C: 156 / 0.52 = 156 * (100 / 52) / 100 = 300. Therefore, the cost price of item A is Rs. 300. Verification / Alternative check: If C = 300, then SP_A = 1.40 * 300 = Rs. 420. SP_B = 0.80 * 420 = Rs. 336. Total SP = 420 + 336 = Rs. 756. Total CP = 300 + 300 = Rs. 600. Profit = 756 - 600 = Rs. 156, which matches the given total profit. Hence the value C = 300 is fully consistent with the problem data. Why Other Options Are Wrong: - If C were 350, total profit would be 0.52 * 350 = 182, not 156. - If C were 400, total profit would be 0.52 * 400 = 208. - If C were 450, total profit would be 0.52 * 450 = 234. - Rs. 250 similarly produces a total profit different from 156. Common Pitfalls: A common mistake is to apply the 20% reduction directly to the cost price of item B instead of applying it to the selling price of item A. Some students also incorrectly average the percentages or treat them as being applied on the combined cost price without separating the items. Another pitfall is to try to work with approximate values rather than expressing everything cleanly in terms of C, which makes solving the equation straightforward. Final Answer: The cost price of item A is Rs. 300.

Question 11

A vendor buys chikoos at the rate of 15 for Rs. 8 and sells them at the rate of 10 for Rs. 6. Based on this buying and selling scheme, what is his percentage gain or loss on the cost price?

Accepted Answer

Introduction / Context: In this question, the vendor purchases and sells chikoos in two different quantity-price combinations, namely “15 for Rs. 8” and “10 for Rs. 6”. These kinds of problems are common in profit and loss sections of quantitative aptitude because they require candidates to compute unit cost price and unit selling price and then compare them. The challenge lies in carefully handling the fractions and correctly determining whether the vendor makes a gain or a loss, and by what percentage relative to cost price. Given Data / Assumptions: - Purchase rate: 15 chikoos for Rs. 8. - Selling rate: 10 chikoos for Rs. 6. - All chikoos are identical; there is no wastage. - We must find the percentage profit or loss on the cost price. Concept / Approach: The essential steps are to compute the cost price (CP) per chikoo and the selling price (SP) per chikoo. Cost price per chikoo is total cost divided by the number purchased in that batch; selling price per chikoo is total selling amount divided by the number sold in that batch. Once CP and SP per unit are known, profit per chikoo = SP - CP. The profit percentage is then Profit% = (Profit / CP) * 100. If SP is greater than CP, there is a gain; if SP is lower than CP, there is a loss. Working with per-unit values makes the logic transparent and avoids confusion about how many chikoos are involved. Step-by-Step Solution: Purchase rate: 15 chikoos for Rs. 8. Cost price per chikoo = 8 / 15 rupees. Selling rate: 10 chikoos for Rs. 6. Selling price per chikoo = 6 / 10 = 3 / 5 rupees = 0.6 rupees. Now compare CP and SP in fraction form. CP per chikoo = 8 / 15 ≈ 0.5333 rupees. SP per chikoo = 3 / 5 = 0.6 rupees. Profit per chikoo = SP - CP = (3 / 5) - (8 / 15). Compute: (3 / 5) - (8 / 15) = (9 / 15) - (8 / 15) = 1 / 15 rupee. Profit percentage = (Profit / CP) * 100 = (1 / 15) / (8 / 15) * 100. Simplify: (1 / 15) * (15 / 8) * 100 = (1 / 8) * 100 = 12.5%. Therefore, the vendor gains 12.5%. Verification / Alternative check: Take a common multiple of 15 and 10, such as 30 chikoos. Cost for 30 chikoos: he buys 15 for Rs. 8, so 30 for Rs. 16. Selling for 30 chikoos: he sells 10 for Rs. 6, so 30 for Rs. 18. Profit on 30 chikoos = 18 - 16 = Rs. 2. Profit% = 2 / 16 * 100 = 12.5%, which matches the earlier calculation. Why Other Options Are Wrong: - 12.5 percent loss is incorrect because SP > CP here, so there is clearly a gain. - 11.11 percent gain or 11.1 percent loss come from mixing up the ratios or using 9-for-10 style approximations. - 10 percent gain is an underestimation that does not match the precise fractional calculation. Common Pitfalls: Some students directly compare 15 and 10 or 8 and 6 without converting to per-unit prices, which leads to wrong conclusions. Another frequent mistake is to calculate profit percentage on the selling price instead of on the cost price. Rounding off decimal approximations too early, instead of working with exact fractions, can cause slight but important errors in the final percentage. Final Answer: The vendor makes a 12.5 percent gain on the cost price.

Question 12

A bookseller buys 500 textbooks for a total of Rs. 20,000. He wants to sell them at a profit in such a way that the total profit is equal to the cost price of 50 textbooks, effectively getting 50 books “free”. At what profit percentage on cost price…

Accepted Answer

Introduction / Context: This question presents a real-life type situation where a bookseller wants to earn a profit equivalent to the cost price of a certain number of books, effectively making those books “free” through his profit. The total cost price and the desired profit amount are both given indirectly. Such problems test your ability to relate total cost, total profit, and number of units to determine the required profit percentage. Understanding that “getting 50 books free” means the profit should equal the cost of 50 books is the key conceptual step. Given Data / Assumptions: - Total number of textbooks bought = 500. - Total cost price of 500 textbooks = Rs. 20,000. - The bookseller wants total profit equal to the cost price of 50 textbooks. - We must find the required profit percentage on cost price. Concept / Approach: First, we compute the cost price per textbook. Then we find the cost price of 50 textbooks, which is the desired total profit. The profit percentage is simply (Desired Profit / Total Cost Price) * 100. Once the profit percentage is known, it tells us how much above cost price the selling price per book should be on average. There is no need to explicitly find the selling price per book, because the question only asks for the percentage profit. Step-by-Step Solution: Total cost price of 500 textbooks = Rs. 20,000. Cost price per textbook = 20,000 / 500. Compute: 20,000 / 500 = 40, so CP per textbook = Rs. 40. Cost price of 50 textbooks = 50 * 40 = Rs. 2,000. The bookseller wants his total profit to be Rs. 2,000. Total cost price of all books = Rs. 20,000. Profit percentage = (Total Profit / Total Cost Price) * 100. So, Profit% = (2,000 / 20,000) * 100. Compute: 2,000 / 20,000 = 1 / 10 = 0.10. Thus, Profit% = 0.10 * 100 = 10%. Verification / Alternative check: If profit is 10% on Rs. 20,000, profit amount = 0.10 * 20,000 = Rs. 2,000. We already saw that the cost price of 50 textbooks is Rs. 2,000. Therefore, with a 10% profit, he gains exactly the cost of 50 textbooks, matching his aim of “getting 50 books free”. This confirms that the required profit percentage is correctly computed as 10%. Why Other Options Are Wrong: - 20% profit would give Rs. 4,000 profit, which equals the cost price of 100 textbooks, not 50. - 15% profit yields Rs. 3,000, which corresponds to the cost of 75 textbooks. - 10.5% and 12% give profits slightly larger than Rs. 2,000, overshooting the target of 50 free books. Common Pitfalls: Some learners misinterpret “50 books free” and think he needs to sell 450 books at cost, rather than understanding that profit must equal the cost of 50 books. Another frequent error is to calculate profit percentage based on the value of 50 books instead of on the value of 500 books. Mixing up the roles of total cost and total profit in the percentage formula can also lead to incorrect answers. Final Answer: He should sell the books at an overall profit of 10% on cost price.

Question 13

The difference between the selling prices of an article when it is sold at 4% profit and at 3% profit is Rs 3. What is the cost price of the article?

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Introduction / Context: This aptitude question tests the basic concept of profit percentage and how small changes in profit affect the selling price of an article. By comparing selling prices at two slightly different profit percentages, we can work backward to find the unknown cost price. Questions like this are common in competitive exams and are designed to check how comfortably you handle percentage based profit and loss relations. Given Data / Assumptions: The article is sold once at 4% profit. The same article is sold once at 3% profit. The difference between the two selling prices is Rs 3. The cost price of the article is the same in both situations. Concept / Approach: The standard relation is: Selling Price (SP) = Cost Price (CP) * (1 + profit_percent / 100). Since only the profit percentage changes, the difference between the two selling prices comes directly from the difference between 4% and 3% profit on the same cost price. That difference is 1% of the cost price. Once we equate that 1% of cost price to Rs 3, we can easily compute the cost price. Step-by-Step Solution: Let the cost price of the article be CP.SP at 4% profit = CP * (1 + 4 / 100) = 1.04 * CP.SP at 3% profit = CP * (1 + 3 / 100) = 1.03 * CP.Difference between selling prices = 1.04 * CP - 1.03 * CP = 0.01 * CP.Given that this difference is Rs 3, so 0.01 * CP = 3.Therefore CP = 3 / 0.01 = 300.So, the cost price of the article is Rs 300. Verification / Alternative check: If CP = Rs 300, then SP at 4% profit is 300 * 1.04 = Rs 312, and SP at 3% profit is 300 * 1.03 = Rs 309. The difference is 312 - 309 = Rs 3, which matches the data given in the question. Hence the calculated cost price is consistent and correct. Why Other Options Are Wrong: Rs 400 would give a 1% difference of Rs 4, not Rs 3, so it does not satisfy the condition. Rs 350 would give a difference of 1% of 350, which is Rs 3.50, again not equal to Rs 3. Rs 100 would give a difference of Rs 1, which is too small. Only Rs 300 gives exactly Rs 3 as 1% of cost price. Common Pitfalls: A common mistake is to treat the difference of 1% as 1 rupee directly or to apply percentages incorrectly to the selling price instead of the cost price. Another error is to misinterpret the profit percentages as absolute rupee differences rather than percentage changes. Always remember that profit percentage is always calculated on the cost price unless clearly specified otherwise. Final Answer: The cost price of the article is Rs 300.

Question 14

An article is listed at Rs 2375. A man buys it after two successive discounts of 50% and 25% and then spends Rs 165 on repairs. If he finally sells the article at a profit of 62.5%, what is its selling price (in rupees)?

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Introduction / Context: This question combines multiple real life business ideas: successive discounts on the marked price, additional repair expenses, and then a target profit on the final effective cost. It tests whether you can track cost price correctly when several changes happen one after another and then convert a required profit percentage into a final selling price. Given Data / Assumptions: Marked price of the article is Rs 2375. Two successive discounts are given: first 50%, then 25% on the reduced price. Repair cost after purchase is Rs 165. The article is later sold at a profit of 62.5% on the total effective cost. We assume no other hidden costs or taxes. Concept / Approach: First we find the price actually paid to buy the article after applying both discounts on the marked price. Then we add the repair cost to get the effective cost price. Once we know the effective cost price, we use the profit formula: SP = CP * (1 + profit_percent / 100). Here profit percentage is 62.5%, which is equal to 62.5 / 100 = 0.625, so the multiplier is 1.625. Step-by-Step Solution: Marked price (MP) = Rs 2375.After first discount of 50%, price becomes 2375 * (1 - 0.50) = 2375 * 0.50 = Rs 1187.50.After second discount of 25% on Rs 1187.50, price becomes 1187.50 * (1 - 0.25) = 1187.50 * 0.75 = Rs 890.625.Repair cost added = Rs 165, so effective cost price = 890.625 + 165 = Rs 1055.625.Required profit = 62.5%, so selling price SP = 1055.625 * (1 + 62.5 / 100) = 1055.625 * 1.625.SP = Rs 1715.390625, which rounds to Rs 1715.39. Verification / Alternative check: We can verify by computing the profit amount directly: Profit = SP - CP = 1715.39 - 1055.625 ≈ 659.765. Now 659.765 / 1055.625 * 100 is approximately 62.5%. The minor difference is only due to rounding at the paise level. This confirms that the selling price of Rs 1715.39 is consistent with a 62.5% profit on the effective cost price. Why Other Options Are Wrong: Values like 1467.60, 1492.60 or 1632.80 correspond to much smaller profit percentages when compared with the effective cost price of about Rs 1055.63. None of them reach close to 62.5% profit. Only 1715.39 gives a profit percentage that matches the condition in the question. Common Pitfalls: Candidates often apply both discounts directly as a single percentage or forget that the second discount is applied on the already reduced price. Another common mistake is to ignore the repair cost when calculating the cost price, which leads to an underestimation of the required selling price. Always remember to include all costs before applying the profit percentage. Final Answer: The required selling price of the article is Rs 1715.39.

Question 15

A shopkeeper sells a table at a 20% discount on its marked price and still earns a profit of 60%. If he sells the same table at a 40% discount on the marked price, what will be his new profit percentage?

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Introduction / Context: This question focuses on the relation between marked price, cost price and selling price when discounts are involved. It is a classic profit and loss problem where the discount is changed, and we are asked to find how the profit percentage changes. Understanding how marked price acts as a bridge between cost price and selling price is crucial in such problems. Given Data / Assumptions: The table has some marked price, say MP. At 20% discount on MP, the shopkeeper still makes 60% profit. We need to find the profit percentage when the discount becomes 40% on the same MP. Cost price of the table remains the same in both situations. Concept / Approach: We use the relations SP = MP * (1 - discount_percent / 100) and SP = CP * (1 + profit_percent / 100). First we relate the 20% discount and 60% profit to form an equation involving MP and CP. From that, we find MP in terms of CP. Then we find the new SP with 40% discount on MP and compute the new profit percentage using the same CP. Step-by-Step Solution: Let cost price of the table be CP and marked price be MP.When discount is 20%, SP1 = MP * 0.80.Given profit at this stage is 60%, so SP1 = CP * 1.60.So, MP * 0.80 = 1.60 * CP, therefore MP = (1.60 / 0.80) * CP = 2 * CP.Now discount is 40%, so new selling price SP2 = MP * 0.60 = 2 * CP * 0.60 = 1.20 * CP.Profit percentage in this case = ((SP2 - CP) / CP) * 100 = ((1.20 * CP - CP) / CP) * 100 = 20%. Verification / Alternative check: Assume a convenient cost price, for example CP = Rs 100. Then MP = Rs 200. With 20% discount, SP1 = 200 * 0.80 = Rs 160 which is a 60% profit on Rs 100. With 40% discount, SP2 = 200 * 0.60 = Rs 120. Profit is Rs 20 on cost Rs 100, that is exactly 20%, which confirms our earlier algebraic solution. Why Other Options Are Wrong: 30%, 35% and 40% would all require higher selling prices than Rs 120 when CP is Rs 100. Since the new SP comes directly from applying 40% discount on the same marked price, none of these higher profit percentages match the computed value. Only 20% is consistent with both the discount and the cost price relationships. Common Pitfalls: Many students mistakenly apply discount directly on cost price or assume that profit percentage decreases by the same percentage as the increase in discount. In reality, discounts work on marked price and profits work on cost price. Keeping these roles separate prevents confusion and mistakes in multi step problems like this. Final Answer: The new profit percentage when the discount is 40% is 20%.

Question 16

The price of a diamond is directly proportional to the square of its weight. A man accidentally breaks a diamond into three pieces in the ratio 3 : 5 : 7 and thereby incurs a loss of Rs 42600. What was the original price of the diamond (in rupees)?

Accepted Answer

Introduction / Context: This question tests your understanding of proportionality and how value can depend on the square of a physical quantity, in this case the weight of a diamond. Diamonds and many other precious items often follow non linear pricing models where larger pieces are disproportionately more valuable than smaller pieces. When such an item is broken into parts, there is a loss because total value no longer follows the same square law as the original single piece. Given Data / Assumptions: Price of a diamond is directly proportional to the square of its weight. The diamond is broken into three parts with weights in the ratio 3 : 5 : 7. The resulting loss due to breaking is Rs 42600. We need to find the original price of the intact diamond. We assume the proportionality constant remains the same before and after breaking. Concept / Approach: If the weight of the full diamond is W, its price is proportional to W^2. When broken into three parts with weights 3k, 5k and 7k, the sum of weights is still W = 3k + 5k + 7k = 15k. The price of each piece is proportional to the square of its weight, so total price after breaking is proportional to 3k squared + 5k squared + 7k squared. The difference between original price and total price after breaking is equal to the loss given in the question. Step-by-Step Solution: Let common factor of weights be k, so the three pieces have weights 3k, 5k and 7k.Total original weight W = 3k + 5k + 7k = 15k.Price is proportional to square of weight, so original price is proportional to (15k)^2 = 225k^2.After breaking, total price is proportional to 3k^2 + 5k^2 + 7k^2 = 9k^2 + 25k^2 + 49k^2 = 83k^2.Loss in terms of proportional units is 225k^2 - 83k^2 = 142k^2.Given actual loss is Rs 42600, so 142k^2 corresponds to Rs 42600.Therefore k^2 = 42600 / 142 = 300.Original price corresponds to 225k^2 = 225 * 300 = Rs 67500. Verification / Alternative check: We can use a simple proportional constant, say 1 rupee per k^2 unit, to visualise the calculation. Original price = 225 units, price after breaking = 83 units, loss = 142 units. If 142 units equal Rs 42600, 1 unit equals Rs 300. Thus original price = 225 * 300 = Rs 67500, exactly as calculated. This confirms the correctness of our result. Why Other Options Are Wrong: Values like 60000 or 75000 do not satisfy the proportional relationship between loss and original price when computed using the ratio based square weights. 11786 is far too small given a loss of Rs 42600. Only Rs 67500 yields a loss equal to Rs 42600 when we recalculate using the square law of pricing. Common Pitfalls: A frequent mistake is to assume that price is directly proportional to weight and not to the square of weight as given. Another error is to use the ratio 3 : 5 : 7 directly on price without squaring the terms. Always pay attention to whether the relationship is linear or involves squares, cubes or higher powers, since this completely changes the computation. Final Answer: The original price of the diamond was Rs 67500.

Question 17

If a saree is sold for Rs 2880, the seller incurs a loss of 10%. At what price (in rupees) should the saree be sold instead in order to earn a profit of 20%?

Accepted Answer

Introduction / Context: This is a straightforward profit and loss question where we move from a known loss situation to a desired profit situation on the same item. The main idea is to first recover the cost price using the loss information and then use that cost price to find the selling price corresponding to the desired profit percentage. Given Data / Assumptions: Selling price with loss is Rs 2880. At this price the seller faces a loss of 10%. The same saree is to be sold to earn a profit of 20%. Cost price of the saree remains constant. Concept / Approach: When there is a loss of 10%, selling price is 90% of cost price. Using SP = CP * (1 - loss_percent / 100), we can determine cost price. After that, to achieve a 20% profit, we use SP = CP * (1 + profit_percent / 100). This two step process, first backward to CP and then forward to new SP, is very typical for such questions. Step-by-Step Solution: Let the cost price of the saree be CP.Given loss is 10%, so SP1 = CP * (1 - 10 / 100) = 0.90 * CP.But SP1 is Rs 2880, so 0.90 * CP = 2880.Therefore CP = 2880 / 0.90 = Rs 3200.Now we want a profit of 20%, so SP2 = CP * (1 + 20 / 100) = 1.20 * CP.SP2 = 1.20 * 3200 = Rs 3840. Verification / Alternative check: Check with the cost price: at CP = Rs 3200, a 10% loss means selling at 90% of CP which is 0.90 * 3200 = Rs 2880, matching the given loss situation. For 20% profit, 1.20 * 3200 = Rs 3840, which is consistent and confirms our answer. Why Other Options Are Wrong: Values like 3480 or 4380 correspond to different profit percentages when compared to the cost price of Rs 3200. For example, 3480 would give only 8.75% profit and 4380 would give about 36.875% profit. 4830 is much higher and would lead to an even larger profit. Only Rs 3840 yields exactly 20% profit. Common Pitfalls: Sometimes students directly adjust the old selling price by adding 30% (10% loss to 20% profit) on 2880, which is incorrect because profit and loss are always calculated on cost price, not on the previous selling price. Always go back to cost price first and then move forward to a new selling price based on the required profit percentage. Final Answer: The saree should be sold for Rs 3840 to earn a 20% profit.

Question 18

A wholesaler sells a good to a retailer at a profit of 5%, and the retailer then sells it to a customer at a profit of 10%. If the customer pays Rs 2000 for the good, what did it cost the wholesaler (in rupees)?

Accepted Answer

Introduction / Context: This problem illustrates a typical trade chain: wholesaler to retailer to customer, with each party adding their own profit margin. The question requires you to work backwards from the final selling price paid by the customer to find the original cost to the wholesaler. It is a good exercise in handling successive percentages and reversing them correctly. Given Data / Assumptions: The wholesaler sells to the retailer at a profit of 5%. The retailer sells to the final customer at a profit of 10%. The final customer pays Rs 2000. We assume that there are no taxes, discounts or additional costs other than the stated profits. Concept / Approach: Let the wholesaler cost price be CPw. The wholesaler sells at 5% profit, so the price to the retailer is CPw * 1.05. The retailer then sells at 10% profit on his cost, so selling price to the customer is CPw * 1.05 * 1.10. This combined factor is 1.155. Since the final price is known, we can divide by this factor to find CPw. This is a classic example of reversing successive percentage increases. Step-by-Step Solution: Let the cost price to the wholesaler be CPw.Price to retailer = CPw * (1 + 5 / 100) = CPw * 1.05.Price to customer = (CPw * 1.05) * (1 + 10 / 100) = CPw * 1.05 * 1.10 = CPw * 1.155.We are given that the customer pays Rs 2000.So, CPw * 1.155 = 2000.Therefore CPw = 2000 / 1.155 ≈ Rs 1731.60. Verification / Alternative check: Take CPw = Rs 1731.60. Wholesaler sells to retailer at 5% profit: price becomes 1731.60 * 1.05 = Rs 1818.18 approximately. Retailer adds 10% profit: 1818.18 * 1.10 ≈ Rs 2000, which matches the given customer price. This confirms that our back calculation is correct and consistent. Why Other Options Are Wrong: Values like 1931.6, 2310.6 or 3210.6, when multiplied by 1.155, do not give Rs 2000. Instead, they would lead to final prices larger or smaller than Rs 2000, which contradicts the given information. Only Rs 1731.6 reproduces the correct end price after applying both profit percentages. Common Pitfalls: Students sometimes subtract percentages directly or treat the total profit as 15% simply added on once, which is not correct because the second profit is calculated on an already increased price. Another common error is to divide by 1.15 instead of 1.155. Always compute the combined multiplier accurately when dealing with successive percentages. Final Answer: The cost price of the good to the wholesaler was approximately Rs 1731.60.

Question 19

When a discount of 25% is given on a wedding gown, the seller still makes a profit of 32%. If instead the discount is reduced to 17% on the same marked price, what will be the new profit percentage?

Accepted Answer

Introduction / Context: This problem again explores the connection between discount and profit on the same item. The wedding gown has a fixed marked price, but changing the discount changes the selling price and therefore the profit percentage. The question checks how well you can move between marked price, cost price and selling price when two different discount situations are given. Given Data / Assumptions: Discount of 25% on the marked price gives a profit of 32%. Discount of 17% on the same marked price is considered next. We need to find the profit percentage in the second case. The cost price and marked price of the gown remain the same in both scenarios. Concept / Approach: Let MP be the marked price and CP be the cost price. When discount is 25%, the selling price is MP * 0.75 and this equals CP * 1.32. From this relation we can express MP in terms of CP. Then for a discount of 17%, the selling price is MP * 0.83. Using the MP obtained earlier, we compute the new selling price and then the new profit percentage by comparing it to CP. Step-by-Step Solution: Let cost price be CP and marked price be MP.With 25% discount, selling price SP1 = MP * (1 - 25 / 100) = 0.75 * MP.Given profit here is 32%, so SP1 = CP * 1.32.Thus 0.75 * MP = 1.32 * CP, so MP = (1.32 / 0.75) * CP = 1.76 * CP.With 17% discount, selling price SP2 = MP * (1 - 17 / 100) = 0.83 * MP.Using MP = 1.76 * CP, SP2 = 0.83 * 1.76 * CP = 1.4608 * CP.Profit percentage in this case = (SP2 - CP) / CP * 100 = (1.4608 * CP - CP) / CP * 100 = 0.4608 * 100 = 46.08%. Verification / Alternative check: Take CP = Rs 100 as a simple assumption. Then MP = 1.76 * 100 = Rs 176. With 25% discount, SP1 = 0.75 * 176 = Rs 132, which is exactly a 32% profit on Rs 100. With 17% discount, SP2 = 0.83 * 176 = Rs 146.608, whose profit on Rs 100 is 46.08%. This numerical check supports our algebraic work. Why Other Options Are Wrong: Values like 43.16%, 49% or 51.03% correspond to different discount or cost price relationships and are not consistent with the derived marked price. Only 46.08% matches the exact profit percentage obtained from the correct formula and the given conditions. Common Pitfalls: One common mistake is to think that a decrease in discount of 8 percentage points always increases profit by exactly 8 percentage points. This is not true because discount works on marked price and profit works on cost price. The correct approach is always to move stepwise through MP and CP with precise multipliers. Final Answer: With a 17% discount, the new profit percentage will be 46.08%.

Question 20

A vendor buys oranges at the rate of 5 for Rs 6 and sells them at the rate of 2 for Rs 3. What is his overall result on this trade in percentage terms (profit or loss)?

Accepted Answer

Introduction / Context: This is a classic cost per unit and selling price per unit type profit and loss question. The vendor changes the quantity in which he buys and sells, and the price per piece changes accordingly. The main test here is whether you can correctly compute cost price per orange and selling price per orange, and then decide the percentage profit or loss. Given Data / Assumptions: The vendor buys 5 oranges for Rs 6. He sells oranges at 2 for Rs 3. We need to determine the profit or loss percentage. We assume there is no wastage or spoilage and that all bought oranges are sold. Concept / Approach: The key idea is to find price per orange in both buying and selling. Cost price per orange is total cost divided by number of oranges purchased. Selling price per orange is total selling price divided by number of oranges sold. Then standard percentage formula is used: Profit% = (SP - CP) / CP * 100. If the result is positive, it is profit, otherwise it is loss. Step-by-Step Solution: Buying rate: 5 oranges cost Rs 6, so cost price per orange = 6 / 5 = Rs 1.20.Selling rate: 2 oranges sold for Rs 3, so selling price per orange = 3 / 2 = Rs 1.50.Profit per orange = SP - CP = 1.50 - 1.20 = Rs 0.30.Profit percentage = (profit per orange / cost price per orange) * 100.Profit percentage = (0.30 / 1.20) * 100 = 0.25 * 100 = 25%.Therefore, the vendor makes a 25 percent gain. Verification / Alternative check: Consider buying 10 oranges. At the buying rate, 10 oranges cost 2 * Rs 6 = Rs 12. Selling 10 oranges at 2 for Rs 3 means 5 groups of 2, each group yielding Rs 3, so total SP = 5 * 3 = Rs 15. Profit = 15 - 12 = Rs 3, and profit percentage = 3 / 12 * 100 = 25%, confirming our earlier calculation. Why Other Options Are Wrong: 20 percent gain would correspond to a smaller difference between SP and CP per orange. 25 percent loss or 20 percent loss would require selling price to be less than cost price, which is not the case here since 1.50 is clearly more than 1.20. Therefore all options showing loss or 20 percent gain are inconsistent with the actual numbers. Common Pitfalls: A common misunderstanding is to compare 5 for 6 and 2 for 3 directly without converting to per unit rates. Some students also mistake 5 and 2 as directly comparable quantities and miscompute ratios. Always reduce such problems to a per item cost and per item selling price to avoid confusion and calculation errors. Final Answer: The vendor makes a 25 percent gain on selling the oranges.

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