Question 1

The profit earned by selling an article for Rs. 832 is equal to the loss incurred by selling the same article for Rs. 448; what should be its selling price to obtain a 50% profit on the cost price?

Accepted Answer

Introduction / Context:This profit and loss problem involves an article sold at two different prices, one resulting in a profit and the other in a loss of equal magnitude. Such questions are classic in aptitude exams and help learners understand how to determine the cost price when profit and loss amounts are equal but the selling prices differ. Once cost price is known, we can easily find any required selling price for a desired profit percentage. Given Data / Assumptions: When the article is sold for Rs. 832, there is a profit. When it is sold for Rs. 448, there is a loss. The profit amount is equal to the loss amount. We need to find the selling price that will give a 50% profit. Cost price is assumed to be the same in all cases. Concept / Approach:Let the cost price be CP and the common magnitude of profit and loss be x. When there is profit, selling price = CP + x. When there is loss, selling price = CP - x. Here, CP + x = 832 and CP - x = 448. Solving these two equations simultaneously will give the values of CP and x. Once CP is known, a 50% profit corresponds to a selling price of 1.5 times CP. This stepwise algebraic method is clean and commonly used. Step-by-Step Solution:Step 1: Let the cost price of the article be CP.Step 2: Let the profit (or loss) amount be x.Step 3: From selling at a profit, CP + x = 832.Step 4: From selling at a loss, CP - x = 448.Step 5: Add these two equations: (CP + x) + (CP - x) = 832 + 448.Step 6: This simplifies to 2CP = 1280.Step 7: Hence CP = 1280 / 2 = Rs. 640.Step 8: Now we need a 50% profit on CP.Step 9: 50% of CP = 0.5 * 640 = Rs. 320.Step 10: Required selling price = CP + 50% of CP = 640 + 320 = Rs. 960. Verification / Alternative check:We can confirm the consistency of CP = 640 with the original data. Profit at selling price 832 is 832 - 640 = Rs. 192. Loss at selling price 448 is 640 - 448 = Rs. 192. Since profit and loss amounts match, CP = 640 is correct. Then for 50% profit, selling price must be 1.5 * 640 = Rs. 960. The result aligns perfectly with the required condition, so there is no contradiction. Why Other Options Are Wrong: Rs. 660 and Rs. 560: These values are much closer to the lower selling price and do not represent a 50% gain over CP. Rs. 1060: This would be far more than a 50% profit. If CP is 640, then 1060 corresponds to a profit of 420, which is 65.625%. Common Pitfalls: Assuming that the average of the two selling prices is the cost price without proper reasoning. In this case that average indeed equals CP only because the profit and loss are equal, but the reasoning should involve algebra. Confusing percentage profit with absolute profit amount. Incorrectly computing 50% of cost price or adding it to CP. Final Answer:The article should be sold for Rs. 960 to earn a 50% profit on the cost price.

Question 2

A retailer cheats both wholesaler and customer by receiving 19% extra quantity from the wholesaler and delivering 15% less quantity to the customer while charging the cost price; what is his effective profit percentage?

Accepted Answer

Introduction / Context:This question is about dishonest trading practices, where a retailer manipulates quantities while keeping the displayed price unchanged. He receives more goods from the wholesaler than he pays for and gives less to the customer than what he charges for. These tricks create a hidden profit. The task is to compute the effective profit percentage that arises purely from these quantity manipulations when the nominal selling price equals the cost price per unit. Given Data / Assumptions: The retailer pays the wholesaler for a nominal quantity but actually receives 19% more quantity. He sells to customers while giving 15% less quantity than what he charges for. He charges customers at the same nominal rate as his cost price per unit. No additional overheads or taxes are mentioned. We must find the net profit percentage based only on the discrepancy between actual and nominal quantities. Concept / Approach:Assume a simple base cost price per unit, for example Rs. 1, and a nominal quantity such as 100 units for which the retailer settles accounts. He pays the wholesaler for 100 units but gets 119 units (19% extra). When selling, he charges the customer for 100 units at cost price but actually gives only 85 units (15% less than 100). The difference between what he pays per actual unit and what he collects per actual unit gives the effective profit percentage. Profit factor is computed as selling price per actual unit divided by cost price per actual unit, and profit percentage is then derived from that ratio. Step-by-Step Solution:Step 1: Assume nominal cost price per unit = Re. 1 for simplicity.Step 2: Wholesaler billing: retailer pays for 100 nominal units at Re. 1 each, so money paid = Rs. 100.Step 3: Actual quantity received from wholesaler = 100 + 19% of 100 = 119 units.Step 4: Effective cost price per actual unit = Total cost / Actual quantity = 100 / 119.Step 5: When selling, retailer charges customers for 100 nominal units at Re. 1 each, so revenue per nominal 100 units = Rs. 100.Step 6: But he actually delivers only 100 - 15% of 100 = 85 units.Step 7: Effective selling price per actual unit = 100 / 85.Step 8: Profit factor per actual unit = (Effective selling price per unit) / (Effective cost price per unit).Step 9: Profit factor = (100 / 85) divided by (100 / 119) = (100 / 85) * (119 / 100) = 119 / 85.Step 10: Convert 119 / 85 to decimal: 119 / 85 = 1.4.Step 11: Hence profit percentage = (1.4 - 1) * 100 = 0.4 * 100 = 40%. Verification / Alternative check:To verify, we can compute actual amounts for a larger example. Suppose the retailer repeats this process many times, so total effective cost is some multiple of 100 / 119 and total revenue is some multiple of 100 / 85 per unit. Since the ratio of selling price to cost price per unit remains 119 / 85, the profit percentage will always be 40%. Therefore, it does not matter what initial quantity we assume; the result is consistent and robust. Why Other Options Are Wrong: 35%: This underestimates the combined effect of getting extra goods and giving short quantity to customers. 42%: Slightly more than the correct value but does not match the precise ratio 119 / 85. 46%: This is far from the true computed profit and has no algebraic justification from the given data. Common Pitfalls: Calculating profit on the nominal 100 units instead of actual units received and delivered. Forgetting that the retailer gains in two ways simultaneously and incorrectly adding or subtracting percentages linearly. Using average of 19% and 15% as the profit percentage, which is conceptually incorrect. Final Answer:The retailer earns an effective profit of 40% by cheating in both purchase and sale quantities while keeping the displayed price at cost price.

Question 3

A shopkeeper sells one third of his goods at a profit of 10%, another one third at a profit of 20% and the remaining one third at a loss of 6%; what is his overall profit percentage on the entire stock?

Accepted Answer

Introduction / Context:This question is about computing overall profit percentage when different parts of the same stock are sold at different profit or loss percentages. The shopkeeper divides his goods into three equal value parts and sells each part under different profit or loss conditions. The aim is to find the net profit percentage on the whole business. This scenario helps learners understand weighted averages in the context of profit and loss. Given Data / Assumptions: The total stock is divided into three equal portions by cost value. First one third is sold at a profit of 10%. Second one third is sold at a profit of 20%. Third one third is sold at a loss of 6%. We assume the three parts have equal cost prices to simplify calculations. We need the overall profit percentage on total cost of all goods. Concept / Approach:Because each portion is one third of the total cost value, the overall profit percentage can be found by taking the simple average of the three individual profit or loss percentages. In general, when identical cost bases are used, overall profit percentage is the arithmetic mean of component percentages. So we simply average 10%, 20% and -6%. Alternatively, we can assume a convenient total cost, compute each part cost, find total selling price and then derive profit percentage. Step-by-Step Solution:Step 1: Let total cost price of all goods be Rs. 300 for easy calculations.Step 2: Then each one third portion has cost price = 300 / 3 = Rs. 100.Step 3: For the first portion, profit = 10% of 100 = Rs. 10, so selling price = 110.Step 4: For the second portion, profit = 20% of 100 = Rs. 20, so selling price = 120.Step 5: For the third portion, loss = 6% of 100 = Rs. 6, so selling price = 94.Step 6: Total selling price = 110 + 120 + 94 = Rs. 324.Step 7: Total cost price = Rs. 300 by assumption.Step 8: Net profit = 324 - 300 = Rs. 24.Step 9: Overall profit percentage = (24 / 300) * 100.Step 10: Simplify 24 / 300 = 0.08, so profit percentage = 8%. Verification / Alternative check:Since each third has equal cost value, we can simply average the three percentages directly: (10 + 20 - 6) / 3. Sum of percentages = 24. Divide by 3 to get 8%. This quick method gives the same result as the detailed calculation above. Therefore, the overall profit percentage is confirmed to be 8%. Why Other Options Are Wrong: 6%: This might be guessed by subtracting the loss directly from one of the profits, but it ignores the actual distribution of gains and losses. 10%: This is just one of the individual profits, not the combined effect. 12%: This value overstates the profit and does not arise from any correct averaging or total calculation. Common Pitfalls: Forgetting that the loss is on one third of the goods and treating it as if it reduces one particular profit directly. Using an incorrect weighted average when the parts are actually equal in cost. Confusing profit percentages on cost with percentages on selling price, which would change the computation completely. Final Answer:The shopkeeper overall makes a profit of 8% on the entire stock of goods.

Question 4

Ajay mixes 15 kg of dal bought at Rs. 14.50 per kg with 10 kg of dal bought at Rs. 13 per kg and sells the entire 25 kg mixture at Rs. 15 per kg; what is his total gain in rupees on this transaction?

Accepted Answer

Introduction / Context:This mixture and profit problem involves combining two types of dal purchased at different rates and then selling the mixture at a single uniform price. The question requires calculation of the total profit in rupees, not just the profit percentage. Such problems test the ability to compute weighted average cost and compare it with the realized selling price for the whole batch. Given Data / Assumptions: Ajay buys 15 kg of dal at Rs. 14.50 per kg. He buys another 10 kg of dal at Rs. 13 per kg. Total mixture quantity = 15 + 10 = 25 kg. He sells the mixture at Rs. 15 per kg. No wastage or extra cost is mentioned. We need to find total gain in rupees. Concept / Approach:The method is to compute the total cost of both types of dal, then compute the total revenue from selling the whole mixture. The difference between total revenue and total cost is the profit. It is important to work with the total amounts first, and only then derive any average if needed. Here the question explicitly asks for the profit in rupees, so we will stop at that value after the calculations. Step-by-Step Solution:Step 1: Cost of first type of dal = 15 kg * Rs. 14.50 per kg.Step 2: Compute 15 * 14.50 = 15 * 14 + 15 * 0.5 = 210 + 7.5 = Rs. 217.50.Step 3: Cost of second type of dal = 10 kg * Rs. 13 per kg = Rs. 130.Step 4: Total cost price of mixture = 217.50 + 130 = Rs. 347.50.Step 5: Total quantity of mixture = 15 + 10 = 25 kg.Step 6: Selling price per kg of mixture = Rs. 15.Step 7: Total selling price = 25 * 15 = Rs. 375.Step 8: Profit (gain) = Total selling price minus Total cost price.Step 9: Profit = 375 - 347.50 = Rs. 27.50. Verification / Alternative check:We can compute the average cost price per kg and then compare it with the selling price per kg. Average cost per kg = Total cost / Total quantity = 347.50 / 25 = 13.90. Selling price per kg = 15. Profit per kg = 15 - 13.90 = Rs. 1.10. Multiply this by total 25 kg to get total profit = 1.10 * 25 = Rs. 27.50. This confirms that both methods give the same profit value, so our calculation is correct. Why Other Options Are Wrong: Rs. 1.10: This is the profit per kg, not the total profit on 25 kg. Rs. 11 and Rs. 16.50: These represent possible partial profits if fewer kilograms were sold, but they do not match the full transaction. Common Pitfalls: Adding the two price rates directly and averaging without weighting according to quantities, which leads to an incorrect average cost. Confusing profit per kg with total profit, especially when one notices Rs. 1.10 as the per kg margin. Rounding off intermediate values too early instead of keeping exact figures like Rs. 217.50. Final Answer:Ajay gains a total of Rs. 27.50 from selling the mixed dal at Rs. 15 per kg.

Question 5

Every year before the festive season, a shopkeeper increases the price of a product by 35% and then offers two successive discounts of 10% and 15%; what is the net percentage profit or loss on the original price?

Accepted Answer

Introduction / Context:This question examines combined percentage changes involving a price increase followed by two successive discounts. Such situations are common in sales and marketing strategies where a marked up price is later shown as discounted. The task is to determine whether the shopkeeper finally makes a profit or a loss with respect to the original price, and by what percentage. Given Data / Assumptions: Original price of the product is assumed to be some base amount, say Rs. 100. Price is first increased by 35% before the festival. Two successive discounts are then applied: first 10%, then 15% on the reduced price. No additional taxes or costs are considered. We need to find the net percentage profit or loss relative to the original price. Concept / Approach:Percentage increase and successive discounts are multiplicative factors on the original price. A 35% increase multiplies the price by 1.35. A 10% discount multiplies by 0.90 and a further 15% discount multiplies by 0.85. The final price factor is therefore original price multiplied by 1.35 * 0.90 * 0.85. Comparing this final price with the original price indicates whether there is a net gain or loss and by what percentage. This approach avoids handling actual rupee values and works entirely with percentage multipliers. Step-by-Step Solution:Step 1: Let the original price of the product be Rs. 100.Step 2: Price is increased by 35%, so new price after increase = 100 * 1.35 = Rs. 135.Step 3: First discount of 10% is applied on Rs. 135.Step 4: Price after first discount = 135 * 0.90 = Rs. 121.50.Step 5: Second discount of 15% is then applied on Rs. 121.50.Step 6: Price after second discount = 121.50 * 0.85.Step 7: Compute 121.50 * 0.85 = 103.275, so final selling price ≈ Rs. 103.28.Step 8: Compare final price with original price Rs. 100.Step 9: Net change = 103.275 - 100 = Rs. 3.275 profit.Step 10: Profit percentage = (3.275 / 100) * 100 = 3.275% ≈ 3.27% gain. Verification / Alternative check:Using the multiplicative factor method, the overall multiplier from original price to final price is 1.35 * 0.90 * 0.85. Compute this: 1.35 * 0.90 = 1.215. Now 1.215 * 0.85 = 1.03275. This means final price is 1.03275 times the original, or 103.275% of the original. Therefore net gain percentage = 103.275 - 100 = 3.275% gain. This matches the stepwise money calculation and confirms that the result is approximately 3.27% gain. Why Other Options Are Wrong: 3.27% loss: This would require final price to be 96.73% of the original, which is not the case here. 4.15% loss or 4.15% gain: These values do not match the accurate combined percentage multiplier 1.03275 and are simply distractor options. Common Pitfalls: Adding percentages linearly, for example 35% minus 10% minus 15% and concluding a 10% rise, which ignores the multiplicative nature of successive changes. Applying both discounts on the original price instead of sequentially, which changes the final price. Incorrect decimal multiplication or rounding too aggressively, which may slightly distort the final percentage. Final Answer:The shopkeeper makes a net 3.27% gain on the original price after increasing the price and then giving the two successive discounts.

Question 6

A sells an article to B at a profit of 20%, B sells it to C at a loss of 25% and C sells it to D at a profit of 40%; if D pays Rs. 252 for the article, how much did A originally pay for it?

Accepted Answer

Introduction / Context:This chained profit and loss question follows an article as it is sold through several people, each making a gain or loss at different percentages. Starting from the final selling price paid by D, we need to work backwards through the percentage changes to recover the original cost price paid by A. This type of question is common in aptitude tests, where it develops an understanding of forward and backward percentage calculations. Given Data / Assumptions: A sells the article to B with a profit of 20% over A cost price. B sells to C at a loss of 25% with respect to B cost. C sells to D at a profit of 40% over C cost. Final price paid by D = Rs. 252. We need to find the amount originally paid by A, which is the initial cost price. Concept / Approach:Backward percentage calculation is best handled by reversing each change step by step. When we know a selling price and a profit percentage, the cost price is given by selling price divided by (1 + profit percentage / 100). When there is a loss, cost price is selling price divided by (1 - loss percentage / 100). Here we start from D price, compute the price at which C bought the article, then the price B paid, and finally the original price A paid. This method ensures clarity at every stage. Step-by-Step Solution:Step 1: Let the price at which C sells the article to D be denoted as SP_CD = Rs. 252.Step 2: C makes a profit of 40% when selling to D.Step 3: So SP_CD = Cost price for C * (1 + 40 / 100) = Cost price for C * 1.4.Step 4: Cost price for C = 252 / 1.4 = Rs. 180.Step 5: Therefore, B sells the article to C for Rs. 180.Step 6: B sells at a loss of 25% to C.Step 7: Thus 180 = Cost price for B * (1 - 25 / 100) = Cost price for B * 0.75.Step 8: Cost price for B = 180 / 0.75 = Rs. 240.Step 9: Therefore, A sells the article to B for Rs. 240.Step 10: A made a profit of 20% when selling to B.Step 11: So 240 = Cost price for A * 1.2.Step 12: Cost price for A = 240 / 1.2 = Rs. 200. Verification / Alternative check:We can verify by moving forward from A cost price. If A cost price is Rs. 200, A sells to B at 20% profit, so B pays 200 * 1.2 = Rs. 240. B incurs a 25% loss when selling to C, so C pays 240 * 0.75 = Rs. 180. C then sells to D at 40% profit, so D pays 180 * 1.4 = Rs. 252. The forward chain exactly reproduces the given final price, confirming that the initial cost of Rs. 200 is correct. Why Other Options Are Wrong: Rs. 196: This is close to Rs. 200 but does not match the percentage transformations when checked forward. Rs. 210 and Rs. 235: These values do not lead to a final price of Rs. 252 when the given profit and loss percentages are applied in sequence. Common Pitfalls: Applying the percentage operations in the wrong direction, for example multiplying instead of dividing when working backwards. Mixing up profit and loss formulas and using 1 + percentage for both cases. Rounding values too early, especially when dealing with fractional costs, which can lead to slight but important errors in later steps. Final Answer:A originally paid Rs. 200 for the article before it passed through B and C to D.

Question 7

A woman goes to the market with Rs. 500 to buy oranges; due to a 10% decrease in the price of oranges, she is able to buy 2 kg more for the same amount; what was the original price per kilogram of oranges?

Accepted Answer

Introduction / Context:This question is a classic application of percentage change in price and corresponding change in quantity for a fixed budget. The woman has a fixed amount of money and, when the price of oranges drops by a certain percentage, she can buy more kilograms than before. We need to work backward from the change in quantity and the price reduction to find the original price per kilogram. Given Data / Assumptions: Total money available with the woman = Rs. 500. Price of oranges decreases by 10%. Because of this price decrease, she can buy 2 kg more oranges with the same Rs. 500. We assume that all money is spent on oranges before and after the price change. We need to determine the original price per kilogram. Concept / Approach:Let the original price per kilogram of oranges be P. Then the original quantity she can buy is 500 / P. After a 10% price decrease, the new price per kilogram becomes 0.9P. At this new price, the quantity she can buy is 500 / (0.9P). According to the question, this new quantity is exactly 2 kg more than the original quantity. This gives a simple equation involving P. Solving that equation yields the original price per kilogram. Step-by-Step Solution:Step 1: Let the original price per kg of oranges be P rupees.Step 2: Original quantity of oranges she can buy = 500 / P kg.Step 3: New price per kg after 10% decrease = 0.9 * P.Step 4: New quantity she can buy at reduced price = 500 / (0.9P) kg.Step 5: According to the problem, the new quantity is 2 kg more than the original quantity.Step 6: So we write the equation: 500 / (0.9P) = 500 / P + 2.Step 7: Simplify left side: 500 / (0.9P) = (500 / P) * (1 / 0.9).Step 8: Let Q = 500 / P; then we have Q * (1 / 0.9) = Q + 2.Step 9: So Q / 0.9 = Q + 2.Step 10: Multiply both sides by 0.9: Q = 0.9Q + 1.8.Step 11: Rearranging: Q - 0.9Q = 1.8, so 0.1Q = 1.8 and Q = 18.Step 12: Recall that Q = 500 / P, so 500 / P = 18.Step 13: Therefore P = 500 / 18 ≈ 27.777..., that is about Rs. 27.78 per kg. Verification / Alternative check:Use P ≈ 27.78. Original quantity = 500 / 27.78 ≈ 18 kg. New price after 10% decrease is 27.78 * 0.9 ≈ 25.00. With new price 25, quantity = 500 / 25 = 20 kg. This is exactly 2 kg more than 18 kg, as required. The options are rounded to two decimal places, so Rs. 27.77 closely matches the calculation and is the best choice. Why Other Options Are Wrong: Rs. 22.77 and Rs. 25.77: These give different original quantities and do not lead to exactly 2 kg difference after a 10% price cut. Rs. 29.77: This would give a smaller original quantity and would not produce the specified 2 kg increase with a 10% decrease in price. Common Pitfalls: Applying the 10% reduction incorrectly, such as subtracting 10 in rupees instead of 10% of the price. Setting up the equation with the difference in price rather than the difference in quantities. Rounding too early in calculations, which can slightly distort the final answer if not handled carefully. Final Answer:The original price of the oranges was approximately Rs. 27.77 per kilogram.

Question 8

A man buys an item for Rs. 1200 and sells it at a loss of 20%; what is the selling price of the item after incurring this loss?

Accepted Answer

Introduction / Context:This is a straightforward profit and loss calculation involving a known cost price and a stated percentage loss. The task is to compute the selling price after reducing the cost price by the given loss percentage. Questions like this are basic but essential for building strong foundations in percentage and commercial arithmetic. Given Data / Assumptions: Cost price (CP) of the item = Rs. 1200. Loss percentage on the item = 20% of cost. No other expenses or hidden costs are mentioned. We need to find the selling price (SP) after the loss. Concept / Approach:When an item is sold at a loss of L%, the selling price is (100 - L)% of the cost price. In decimal form, SP = CP * (1 - L / 100). Here L = 20, so SP = CP * 0.80. By multiplying 1200 by 0.80, we get the required selling price. This simple formula is widely used in profit and loss questions. Step-by-Step Solution:Step 1: Cost price of the item = Rs. 1200.Step 2: Given loss percentage = 20%.Step 3: Selling price as a percentage of cost = 100% - 20% = 80% of cost.Step 4: Express 80% in decimal form as 0.80.Step 5: Selling price SP = CP * 0.80 = 1200 * 0.80.Step 6: Compute 1200 * 0.80 = Rs. 960.Step 7: Therefore, the item is sold for Rs. 960 after a 20% loss. Verification / Alternative check:We can also compute the loss amount directly. Loss = 20% of 1200 = 0.20 * 1200 = Rs. 240. Subtracting this loss from cost price gives SP = 1200 - 240 = Rs. 960. Both methods agree and confirm that Rs. 960 is the correct selling price corresponding to a 20% loss. Why Other Options Are Wrong: Rs. 660: This would represent a loss of 1200 - 660 = 540, which is a 45% loss. Rs. 760: This would be a loss of 440, which is about 36.67% loss. Rs. 860: This is a loss of 340, which corresponds to about 28.33% loss. Common Pitfalls: Subtracting 20 rupees instead of 20% of the cost price. Accidentally adding the loss percentage instead of subtracting it. Confusing percentage of cost with percentage of selling price, which can lead to reversed calculations. Final Answer:The selling price of the item after a 20% loss on Rs. 1200 is Rs. 960.

Question 9

A shopkeeper fixes the marked price of an item 35% above its cost price; what percentage of discount should be allowed on the marked price so that he still gains 8% on the cost price?

Accepted Answer

Introduction / Context:This question explores the relationship between cost price, marked price, discount and final gain. The shopkeeper increases the marked price above cost and later allows a discount but still wants an overall profit. Such questions are common in commercial mathematics because they reflect real retail pricing strategies and test understanding of how multiple percentage changes interact. Given Data / Assumptions: Marked price (MP) is 35% above cost price (CP). Desired gain on cost price = 8%. A single discount percentage is applied on the marked price. We need to find the discount percentage that ensures an 8% profit overall. No additional taxes or overheads are mentioned. Concept / Approach:We can assume a convenient cost price, for example CP = Rs. 100. Then the marked price becomes 35% more than 100, that is Rs. 135. Let the discount rate on this marked price be d%. After discount, selling price SP will be MP * (1 - d / 100). We want SP to be equal to CP multiplied by 1.08, that is, 108 when CP is 100. Equating SP to 108 allows us to solve for d, the required discount percentage. Step-by-Step Solution:Step 1: Assume cost price CP = Rs. 100 for convenience.Step 2: Marked price MP = CP * (1 + 35 / 100) = 100 * 1.35 = Rs. 135.Step 3: Let discount rate be d%. Then selling price SP = MP * (1 - d / 100).Step 4: The desired gain is 8%, so SP should also equal CP * 1.08 = 100 * 1.08 = Rs. 108.Step 5: Set up the equation: 135 * (1 - d / 100) = 108.Step 6: Divide both sides by 135: 1 - d / 100 = 108 / 135.Step 7: Simplify 108 / 135 = 0.8.Step 8: So 1 - d / 100 = 0.8, which implies d / 100 = 0.2.Step 9: Therefore d = 0.2 * 100 = 20%. Verification / Alternative check:If CP = 100 and discount is 20%, then MP = 135 and SP = 135 * 0.80 = 108. The profit is SP - CP = 108 - 100 = 8 rupees, which is an 8% gain on the cost price. This matches the desired condition perfectly and confirms that a 20% discount is the correct value. Why Other Options Are Wrong: 18%: This would give SP = 135 * 0.82 = 110.7, resulting in a 10.7% profit, which is higher than required. 22%: This would give SP = 135 * 0.78 = 105.3, which corresponds to a 5.3% profit, less than the desired 8%. 24%: This would give SP = 135 * 0.76 = 102.6, only a 2.6% profit. Common Pitfalls: Applying the 8% gain on marked price instead of cost price, which changes the target selling price. Confusing discount percentage with profit percentage and adding or subtracting them incorrectly. Making arithmetic mistakes when simplifying 108 / 135 or solving for the discount. Final Answer:The shopkeeper should allow a discount of 20% on the marked price to gain 8% on cost price.

Question 10

A woman sells 20 articles for Rs. 160 and incurs a loss of 40%; how many such articles must she sell for Rs. 240 in order to earn a profit of 20%?

Accepted Answer

Introduction / Context:This question connects loss in one selling situation with profit in another, both involving the same type of article. First, the woman sells a certain number of articles at a loss, which lets us compute the cost price per article. Then, we find how many articles she must sell at a different total amount to achieve a desired profit percentage. This is a typical profit and loss problem that blends unit cost and total transaction analysis. Given Data / Assumptions: She sells 20 articles for Rs. 160. On this sale she incurs a loss of 40%. She wants to earn a profit of 20% on future sales. We need to find how many articles must be sold for Rs. 240 to earn this 20% profit. Cost price per article remains constant. Concept / Approach:First, we find the selling price per article in the first case, then use the given loss percentage to find the cost price per article. After we know the cost price per article, we compute the selling price per article that corresponds to a 20% profit. Finally, we divide the total desired revenue of Rs. 240 by this per unit selling price to find the number of articles required. This sequence ensures that both loss and profit conditions are properly connected through the same cost price. Step-by-Step Solution:Step 1: In the first scenario, 20 articles sell for Rs. 160.Step 2: Selling price per article in the first scenario = 160 / 20 = Rs. 8.Step 3: She incurs a loss of 40% at this selling price.Step 4: When loss is 40%, selling price = 60% of cost price.Step 5: Therefore, 8 = 0.60 * Cost price per article.Step 6: Cost price per article = 8 / 0.60 = 8 / 0.6 = Rs. 13.33 approximately (or exactly 40 / 3).Step 7: Now she wants to earn a profit of 20%.Step 8: For 20% profit, selling price per article = Cost price * 1.20.Step 9: Selling price per article for 20% profit = (40 / 3) * 1.20 = (40 / 3) * (6 / 5) = 16.Step 10: So, required selling price per article to get 20% profit is Rs. 16.Step 11: She wants total revenue of Rs. 240 in this scenario.Step 12: Number of articles needed = 240 / 16 = 15. Verification / Alternative check:We can verify by checking the total cost and profit for 15 articles. Cost per article = Rs. 40 / 3. Total cost for 15 articles = 15 * (40 / 3) = 200. Total selling price = 15 * 16 = 240. Profit = 240 - 200 = Rs. 40. Profit percentage = (40 / 200) * 100 = 20%. Thus the requirement of 20% profit is satisfied when selling 15 articles for Rs. 240. Why Other Options Are Wrong: 16, 17, 14: These values give per article selling prices of 240 / 16 = 15, 240 / 17 (approximately 14.12) and 240 / 14 (approximately 17.14) respectively. None of these match the required Rs. 16 per article that corresponds to exactly 20% profit based on the true cost price. Common Pitfalls: Using average of loss and profit percentages directly, which is not valid. Forgetting to convert loss percentage into a relationship between cost price and selling price correctly. Rounding cost price too early instead of leaving it as an exact fraction, leading to slight errors in final division. Final Answer:She must sell 15 articles for Rs. 240 to earn a profit of 20% on her cost price.

Question 11

The cash difference between the selling prices of an article at a profit of 4% and at a profit of 6% is Rs. 3; what is the ratio of these two selling prices?

Accepted Answer

Introduction / Context:This profit and loss question relates the difference between two selling prices at different profit percentages on the same article. The fixed cash difference in selling prices allows us to determine the cost price and then the actual selling prices. Finally, the ratio of these two selling prices is asked. Such problems strengthen the understanding of how small changes in profit percentage translate into cash differences. Given Data / Assumptions: An article is sold at a profit of 4% in one case. The same article is sold at a profit of 6% in another case. The difference between these two selling prices is Rs. 3. Cost price of the article is the same in both cases. We need to find the ratio of the selling price at 4% profit to the selling price at 6% profit. Concept / Approach:Let the cost price of the article be CP. Then, selling price at 4% profit is SP1 = 1.04 * CP and selling price at 6% profit is SP2 = 1.06 * CP. The difference SP2 minus SP1 equals 0.02 * CP, which is given as Rs. 3. From this relation, we can determine CP. Once CP is known, SP1 and SP2 can be calculated and their ratio simplified to the lowest terms. This yields the required ratio. Step-by-Step Solution:Step 1: Let cost price be CP rupees.Step 2: Selling price at 4% profit, SP1 = 1.04 * CP.Step 3: Selling price at 6% profit, SP2 = 1.06 * CP.Step 4: Difference SP2 - SP1 = (1.06 * CP) - (1.04 * CP) = 0.02 * CP.Step 5: Given that this difference equals Rs. 3, so 0.02 * CP = 3.Step 6: Therefore CP = 3 / 0.02 = 150.Step 7: Compute SP1 = 1.04 * 150 = 156.Step 8: Compute SP2 = 1.06 * 150 = 159.Step 9: Ratio SP1 : SP2 = 156 : 159.Step 10: Simplify this ratio by dividing both numbers by their greatest common divisor which is 3: 156 / 3 = 52 and 159 / 3 = 53.Step 11: Therefore, the ratio of the selling prices is 52 : 53. Verification / Alternative check:If the ratio is 52 : 53, assume SP1 = 52k and SP2 = 53k for some constant k. The difference is k. For this to equal Rs. 3, k must be 3. Then SP1 = 156 and SP2 = 159. Check also that these correspond to 4% and 6% profit on the same cost price. If CP is 150, 4% profit gives SP1 = 150 * 1.04 = 156 and 6% profit gives SP2 = 150 * 1.06 = 159. This confirms that our values and the resulting ratio are correct. Why Other Options Are Wrong: 51:52, 53:54, 54:55: None of these ratios are consistent with the known difference of Rs. 3 and the given profits of 4% and 6%. They either lead to a different cost price or a different cash difference. Common Pitfalls: Taking the difference of percentages 6% and 4% but not properly translating that into 0.02 * CP in rupees. Incorrectly solving 0.02 * CP = 3 and getting the wrong cost price. Forgetting to simplify the final ratio to its lowest terms. Final Answer:The ratio of the two selling prices at 4% and 6% profit is 52:53.

Question 12

The cost of three cricket balls equals the cost of two pairs of leg pads; the cost of three pairs of leg pads equals the cost of two pairs of gloves, and the cost of three pairs of gloves equals the cost of two cricket bats; if one cricket bat costs…

Accepted Answer

Introduction / Context:This question presents a chain of proportional cost relationships between cricket balls, leg pads, gloves and bats. By expressing everything in terms of one variable and using the known cost of a bat, we can work backward to find the cost of a single ball. It is a typical algebraic application of ratios and proportionality used in aptitude examinations. Given Data / Assumptions: Cost of 3 cricket balls equals the cost of 2 pairs of leg pads. Cost of 3 pairs of leg pads equals the cost of 2 pairs of gloves. Cost of 3 pairs of gloves equals the cost of 2 cricket bats. Cost of 1 cricket bat = Rs. 54. We are asked to find the cost of 1 cricket ball. Concept / Approach:Let the cost of one cricket ball be B, cost of one pair of leg pads be L, cost of one pair of gloves be G, and cost of one bat be T. The given relationships can be written as linear equations: 3B = 2L, 3L = 2G, and 3G = 2T. We also know T = 54. By solving this chain stepwise, we can express B in terms of T and thus compute its numerical value. This approach uses simple algebra and careful substitution. Step-by-Step Solution:Step 1: Define variables as follows: B = cost of one ball, L = cost of one pair of leg pads, G = cost of one pair of gloves, T = cost of one bat.Step 2: From the problem, cost of 3 balls equals cost of 2 pairs of leg pads: 3B = 2L.Step 3: Thus, L = (3 / 2) * B.Step 4: Cost of 3 pairs of leg pads equals cost of 2 pairs of gloves: 3L = 2G.Step 5: Substitute L into 3L = 2G: 3 * (3 / 2) * B = 2G.Step 6: This simplifies to (9 / 2) * B = 2G, so G = (9 / 4) * B.Step 7: Cost of 3 pairs of gloves equals cost of 2 bats: 3G = 2T.Step 8: Substitute G: 3 * (9 / 4) * B = 2T.Step 9: This gives (27 / 4) * B = 2T.Step 10: So B = (2T * 4) / 27 = (8T) / 27.Step 11: Given T = 54, substitute: B = (8 * 54) / 27.Step 12: Compute (8 * 54) / 27 = 8 * (54 / 27) = 8 * 2 = Rs. 16. Verification / Alternative check:We can verify by computing the costs up the chain. If one ball costs Rs. 16, then three balls cost 3 * 16 = Rs. 48. So two pairs of leg pads cost Rs. 48 and one pair costs 24. Then three pairs of leg pads cost 3 * 24 = Rs. 72, which equals cost of two pairs of gloves. So one pair of gloves costs 36. Three pairs of gloves cost 3 * 36 = Rs. 108, which should equal the cost of two bats, so each bat costs 108 / 2 = Rs. 54, exactly as given. The relationships are all satisfied, confirming our calculations. Why Other Options Are Wrong: Rs. 12, Rs. 14, Rs. 18: None of these values produce a consistent chain with the given relations when propagated to the bat cost of Rs. 54. They all lead to mismatch at some step. Common Pitfalls: Inverting ratios incorrectly, for example writing 2L = 3B as L = (2 / 3) * B instead of (3 / 2) * B. Mixing up the number of units (for example, confusing 3 balls and 3 pairs of pads). Not simplifying fractions cleanly when solving for B in terms of T. Final Answer:The cost of one cricket ball is Rs. 16.

Question 13

A person sells two cows for Rs. 9900 each; on one cow he gains 10% and on the other he loses 20%; which of the following statements about his overall result is correct?

Accepted Answer

Introduction / Context:This profit and loss problem shows that having a gain on one item and a loss on another item, even at different percentages, does not necessarily cancel out. The trader sells both cows at the same price but with different percentage outcomes. The question asks us to determine his overall financial result and to match it with the most appropriate statement among the options. Given Data / Assumptions: The person sells each of the two cows for Rs. 9900. On the first cow he gains 10%. On the second cow he loses 20%. We need to determine whether he has an overall gain, overall loss or breaks even, and compare with given statements. Concept / Approach:Profit or loss percentage is calculated on cost price, so we must find individual cost prices for both cows from their selling prices and given percentages. For the cow sold at profit, cost price is selling price divided by 1 plus profit percentage. For the cow sold at loss, cost price is selling price divided by 1 minus loss percentage. Summing both cost prices gives total cost. Summing both selling prices gives total revenue. Comparing total revenue with total cost tells us the net result in rupees and whether it is a profit or loss. Step-by-Step Solution:Step 1: Selling price of first cow, SP1 = Rs. 9900 with a gain of 10%.Step 2: If profit is 10%, then SP1 = 1.10 * Cost price of first cow.Step 3: Therefore, Cost price of first cow, CP1 = 9900 / 1.10 = Rs. 9000.Step 4: Selling price of second cow, SP2 = Rs. 9900 with a loss of 20%.Step 5: If loss is 20%, then SP2 = 0.80 * Cost price of second cow.Step 6: Therefore, Cost price of second cow, CP2 = 9900 / 0.80 = Rs. 12375.Step 7: Total cost price = CP1 + CP2 = 9000 + 12375 = Rs. 21375.Step 8: Total selling price = SP1 + SP2 = 9900 + 9900 = Rs. 19800.Step 9: Net result = Total selling price minus Total cost price = 19800 - 21375 = -1575.Step 10: The negative sign shows a loss. So he loses Rs. 1575 overall. Verification / Alternative check:We can also compute the individual profit and loss in rupees and then combine them. Profit on first cow = SP1 - CP1 = 9900 - 9000 = Rs. 900. Loss on second cow = CP2 - SP2 = 12375 - 9900 = Rs. 2475. Net effect = 900 profit minus 2475 loss = 1575 loss. This matches the earlier calculation, confirming that the overall outcome is a loss of Rs. 1575, not Rs. 200 or zero. Why Other Options Are Wrong: He gained Rs. 200: This is incorrect because detailed calculations show a net loss, not a gain. He lost Rs. 200: Although he does lose money, the actual loss is Rs. 1575, not Rs. 200. He neither gained nor lost: A gain on one cow and a loss on the other do not cancel because the cost prices are different. Common Pitfalls: Assuming that a 10% gain and 20% loss on equal selling prices cancel into a small or zero net effect without doing proper calculations. Using selling prices directly to compute profit and loss percentages instead of cost prices. Making arithmetic mistakes in division when finding cost prices from the given percentages. Final Answer:The trader suffers a loss of Rs. 1575, which does not match any of the specified amounts, so the correct choice is None of the above.

Question 14

Goods are purchased for Rs. 450. One third of the goods is sold at a loss of 10%. At what gain percentage should the remaining goods be sold so that the overall profit on the entire transaction is 20%?

Accepted Answer

Introduction / Context: Profit and loss questions often involve situations where part of the stock is sold at one profit or loss percent and the rest at another rate. To achieve a target overall gain, we must correctly combine the partial selling prices. This question tests understanding of total cost price, partial selling prices and the concept of overall percentage profit on the whole transaction. Given Data / Assumptions: Total cost price (CP) of goods = Rs. 450. One third of the goods is sold at a loss of 10%. Two thirds of the goods remain and are sold at some gain percentage. Required overall profit on the entire transaction = 20% of total cost price. All goods are identical and cost is proportional to quantity. Concept / Approach: The key idea is that overall profit depends on total selling price (SP) compared to total cost price. We first find the CP and SP of the part sold at a loss. Then we use the required overall SP (calculated from 20% gain on the total CP) to determine how much SP must come from the remaining goods. From that we can compute the gain percentage on the remaining part by comparing its SP with its CP. Step-by-Step Solution: Step 1: CP of one third of the goods = (1/3) * 450 = Rs. 150. Step 2: This part is sold at 10% loss, so SP on this part = 150 * (1 - 10/100) = 150 * 0.9 = Rs. 135. Step 3: CP of the remaining two thirds = 450 - 150 = Rs. 300. Step 4: Required overall profit = 20% of 450 = 0.20 * 450 = Rs. 90. Step 5: Therefore, required total SP for 20% gain = 450 + 90 = Rs. 540. Step 6: SP needed from the remaining goods = 540 - 135 = Rs. 405. Step 7: Gain on remaining goods = SP - CP = 405 - 300 = Rs. 105. Step 8: Gain percentage on remaining goods = (105 / 300) * 100 = 35%. Verification / Alternative check: We can verify by recomputing the entire transaction. One third sold for Rs. 135, two thirds sold for Rs. 405, giving total SP = 135 + 405 = Rs. 540. Comparing with total CP of Rs. 450, profit = 540 - 450 = Rs. 90. Profit percent = (90 / 450) * 100 = 20%, which matches the requirement. Hence 35% gain on the remaining goods is correct. Why Other Options Are Wrong: A gain of 28%, 22%, 19% or 30% on the remaining goods would produce a total SP different from Rs. 540 and therefore a different overall profit percent. Only 35% generates exactly 20% profit on the whole transaction, so the other options are numerically inconsistent with the given conditions. Common Pitfalls: Learners sometimes average percentages directly instead of working with actual money values. Another common mistake is to apply the 20% overall gain only to the remaining goods instead of the entire lot. Always compute CP and SP for each part separately, then combine them to check the overall profit or loss. Final Answer: The remaining goods must be sold at a gain of 35% to obtain 20% profit on the whole transaction.

Question 15

A shopkeeper buys 4 mangoes for Rs. 6 and sells them at a rate of 4 mangoes for Rs. 4. What is the percentage of profit or loss made by the shopkeeper on this transaction?

Accepted Answer

Introduction / Context: This is a basic profit and loss question involving unitary method. Instead of directly giving the cost price or selling price of one item, the question gives the price for a group of identical items. To find the exact profit or loss percentage, we convert these group prices into per unit cost and per unit selling price and then compare them. Given Data / Assumptions: Buying rate: 4 mangoes for Rs. 6. Selling rate: 4 mangoes for Rs. 4. Mangoes are identical and of the same quality. We assume there are no extra expenses such as transport or wastage. The objective is to find whether there is a profit or a loss and its percentage. Concept / Approach: Profit or loss percentage is always calculated on the cost price. First, find the cost price of one mango by dividing the total cost by the number of mangoes bought. Then, find the selling price of one mango in the same way. By comparing the selling price with the cost price, we decide whether this is a profit or a loss. Finally, we use the formula for percentage loss or profit based on the difference between cost and selling prices. Step-by-Step Solution: Step 1: Cost price (CP) of 4 mangoes = Rs. 6. Step 2: CP of 1 mango = 6 / 4 = Rs. 1.50. Step 3: Selling price (SP) of 4 mangoes = Rs. 4. Step 4: SP of 1 mango = 4 / 4 = Rs. 1.00. Step 5: Since SP < CP, the shopkeeper incurs a loss. Step 6: Loss per mango = CP - SP = 1.50 - 1.00 = Rs. 0.50. Step 7: Loss percentage = (Loss / CP) * 100 = (0.50 / 1.50) * 100. Step 8: Simplify: 0.50 / 1.50 = 1/3, so loss percentage = (1/3) * 100 = 33.333% (approximately). Verification / Alternative check: Consider buying and selling 12 mangoes to avoid fractions. CP for 12 mangoes = 3 sets of 4 mangoes = 3 * Rs. 6 = Rs. 18. SP for 12 mangoes = 3 sets of 4 mangoes sold = 3 * Rs. 4 = Rs. 12. Loss on 12 mangoes = 18 - 12 = Rs. 6. Loss percentage = (6 / 18) * 100 = 33.333%, which confirms the earlier calculation. Why Other Options Are Wrong: Loss percentages like 36.333%, 33.666% or 36.666% do not match the exact fraction 1/3 of the cost price. The option 25.000% is much smaller than the true value. Only 33.333% is consistent with both unitary method and scaled computation using 12 mangoes. Common Pitfalls: Some learners mistakenly compute profit or loss on the selling price instead of the cost price, or mix up the two group rates. Others average 6 and 4 or compare the groups directly without converting to per unit values. Always reduce the situation to one item and then apply the correct percentage formula to get accurate results. Final Answer: The shopkeeper makes a 33.333% loss on selling the mangoes.

Question 16

In a certain store, the profit is 320% of the cost price of an item. If the cost price increases by 25% but the selling price remains unchanged, approximately what percentage of the selling price is now the profit?

Accepted Answer

Introduction / Context: This question tests understanding of profit as a percentage of cost versus profit as a percentage of selling price. Initially, a very high profit is made relative to cost price. When the cost price increases but the selling price is held constant, the profit reduces, and the problem asks for this reduced profit expressed as a percentage of the selling price. This is a useful concept in commercial mathematics and retail pricing. Given Data / Assumptions: Initial profit = 320% of cost price. Therefore, initially, profit = 3.2 times cost price. So initial selling price = cost price + profit. Cost price increases by 25%. Selling price remains constant at its original value. We must express the new profit as a percentage of the (unchanged) selling price. Concept / Approach: Let the original cost price be C. A profit of 320% of C means profit = 3.2 * C. Hence, initial selling price SP = C + 3.2C = 4.2C. When cost price increases by 25%, new cost price becomes 1.25C, while SP stays at 4.2C. The new profit is SP - new cost = 4.2C - 1.25C. Finally, the required percentage is (new profit / SP) * 100. Because C cancels out, we can work symbolically without needing actual numeric cost. Step-by-Step Solution: Step 1: Let original cost price = C. Step 2: Given profit = 320% of C, so profit = 3.2C. Step 3: Initial selling price SP = C + 3.2C = 4.2C. Step 4: New cost price after 25% increase = C * 1.25 = 1.25C. Step 5: Selling price is unchanged at SP = 4.2C. Step 6: New profit = SP - new cost = 4.2C - 1.25C = 2.95C. Step 7: Required profit percentage on SP = (2.95C / 4.2C) * 100. Step 8: The factor C cancels, so percentage = (2.95 / 4.2) * 100 ≈ 70.24%. Step 9: Approximating, this is about 70% of the selling price. Verification / Alternative check: Take a convenient value, for example C = Rs. 100. Then original profit = 320% of 100 = Rs. 320. Initial SP = 100 + 320 = Rs. 420. New CP after 25% rise = 125. New profit = 420 - 125 = Rs. 295. Profit as percentage of SP = (295 / 420) * 100 ≈ 70.24%, confirming our symbolic calculation and justifying the rounded answer of 70% as the closest option. Why Other Options Are Wrong: An 80% or 90% profit on the selling price would require the profit to be 0.8 or 0.9 times 420, which does not match 295. The value 60% is too low compared to the actual fraction of about 70.24%. Therefore, only 70% is a reasonable approximation based on the calculations. Common Pitfalls: Students sometimes confuse profit as a percentage of cost price with profit as a percentage of selling price, or misinterpret 320% profit as selling price being 320% of cost. Another frequent error is to increase the cost and selling prices together instead of holding the selling price constant as stated. Using a variable for cost and following the algebra carefully avoids these mistakes. Final Answer: After the cost increase, the profit is approximately 70% of the selling price.

Question 17

In a cloth showroom during the festival season, a servant's payment for 12 days is Rs. 400 plus one shirt. The servant leaves after working for 9 days and receives Rs. 280 and a shirt. What is the price of the shirt in rupees?

Accepted Answer

Introduction / Context: This is a typical linear equation question from profit and wage distribution problems. The salary package includes both cash and a non cash component, namely a shirt. When the servant leaves early, he still receives a shirt plus some cash. Using the idea that wages are proportional to days worked, we can find the monetary value of the shirt by equating the pay for 9 days to a proportion of the 12 day package. Given Data / Assumptions: Payment for 12 days of work = Rs. 400 plus one shirt. Payment for 9 days of work = Rs. 280 plus one shirt. Daily wage is assumed to be uniform over the period. Value of the shirt is the same in both cases. We need to find the price of the shirt. Concept / Approach: Think of the combined payment (cash plus shirt) as the total wage for 12 days. The worker should get 9/12 of that total for 9 days of work. The problem gives the 9 day payment explicitly, so we set up an equation relating the proportional wage for 9 days to the actual cash plus shirt he receives. From that equation, we isolate the value of the shirt. This is a direct application of proportional reasoning and simple algebra. Step-by-Step Solution: Step 1: Let the price of the shirt be S rupees. Step 2: Total wage for 12 days = Rs. 400 + S. Step 3: Since wages are proportional to days, wage for 9 days should be (9/12) * (400 + S) = (3/4) * (400 + S). Step 4: The servant actually receives Rs. 280 + S for 9 days. Step 5: Set up the equation: (3/4) * (400 + S) = 280 + S. Step 6: Multiply both sides by 4: 3 * (400 + S) = 4 * (280 + S). Step 7: Expand: 1200 + 3S = 1120 + 4S. Step 8: Rearrange: 1200 - 1120 = 4S - 3S, so 80 = S. Step 9: Therefore, price of the shirt = Rs. 80. Verification / Alternative check: If the shirt costs Rs. 80, then total wage for 12 days = 400 + 80 = Rs. 480. Daily wage = 480 / 12 = Rs. 40. For 9 days, the worker should receive 9 * 40 = Rs. 360. According to the payment structure, he gets 280 cash and a shirt worth 80, total 360, which matches perfectly. This confirms the correctness of S = 80. Why Other Options Are Wrong: If S were Rs. 120, 70, 100 or 60, the 9 day payment would not equal three quarters of the 12 day payment, breaking the proportionality condition. Only Rs. 80 maintains consistent daily wages under both scenarios, so the other options are inconsistent with equal pay per day. Common Pitfalls: A common mistake is to treat the Rs. 400 and the shirt separately, forgetting to scale the combined value when moving from 12 to 9 days. Some learners subtract 280 from 400 directly without considering that the shirt appears in both payments. Always express the total wage that includes both cash and non cash benefits before applying proportional reasoning. Final Answer: The price of the shirt is Rs. 80.

Question 18

By selling an article for Rs. 800, a shopkeeper makes a profit of 25% on its cost price. At what price should he sell the same article in order to incur a loss of 25% on the cost price?

Accepted Answer

Introduction / Context: This question is a straightforward application of profit and loss percentage on the same cost price. First, the shopkeeper sells the article at a profit. We use that information to determine the cost price. Then we are asked to find the selling price that would result in a specific loss percentage on that same cost price. This is common in exam questions that check basic understanding of percentage changes applied to cost price. Given Data / Assumptions: Selling price with profit = Rs. 800. Profit at this price = 25% of cost price. We assume a single fixed cost price for the article. Required: selling price that gives a 25% loss on the same cost price. All transactions are independent but based on the same cost price. Concept / Approach: If profit is 25% of cost price, then selling price equals 125% of cost price. Using SP = 1.25 * CP and the given selling price, we find CP. For the required situation, a 25% loss means selling price should be 75% of cost price. Thus we multiply the cost price by 0.75. Working entirely in terms of cost price ensures the calculation is systematic and avoids mistakes with direct proportionality on selling price. Step-by-Step Solution: Step 1: Let cost price = CP. Step 2: Given that a 25% profit gives SP = Rs. 800, so 800 = CP * (1 + 25/100) = CP * 1.25. Step 3: Therefore, CP = 800 / 1.25. Step 4: Compute CP: 800 / 1.25 = 800 * (4/5) = 640. Step 5: To get a 25% loss, SP must be 75% of CP, i.e., SP = 0.75 * CP. Step 6: Required SP = 0.75 * 640 = 480. Step 7: Hence, the article must be sold for Rs. 480 to incur a 25% loss. Verification / Alternative check: Check both scenarios explicitly. With CP = Rs. 640 and SP = Rs. 800, profit = 800 - 640 = Rs. 160, profit percentage = (160 / 640) * 100 = 25%. With SP = Rs. 480, loss = 640 - 480 = Rs. 160, loss percentage = (160 / 640) * 100 = 25%. The symmetry in gain and loss confirms that the calculations are correct. Why Other Options Are Wrong: Selling the article for Rs. 720 or Rs. 640 would still give a profit or no loss on a cost price of Rs. 640. A price of Rs. 540 would generate a smaller loss percentage, not exactly 25%, while Rs. 600 would give only a modest loss or even very small loss relative to CP. Only Rs. 480 yields a 25% loss. Common Pitfalls: A frequent error is to treat the given selling price of Rs. 800 as 125% of Rs. 800, or to decrease that directly by 25% instead of first computing the cost price. Another mistake is to apply 25% loss to the selling price rather than the cost price. Always remember that both profit and loss percentages are applied on the cost price unless stated otherwise. Final Answer: The shopkeeper should sell the article for Rs. 480 to incur a 25% loss on the cost price.

Question 19

A sweet seller sells three fifths of his sweets at a profit of 10% and the remaining sweets at a loss of 5%. If his overall profit on the entire transaction is Rs. 1500, what is the total cost price of the sweets?

Accepted Answer

Introduction / Context: This is a classic mixed transaction problem in profit and loss. A trader sells part of the goods at a gain and the remainder at a loss, yet overall he makes a net profit. The question asks us to compute the total cost price from the known overall profit and the given profit and loss percentages on the respective parts. Understanding weighted profit and loss is key here. Given Data / Assumptions: Fraction of sweets sold at profit = 3/5 of total quantity. Profit on this part = 10%. Remaining 2/5 of sweets are sold at a loss of 5%. Overall profit on all sweets = Rs. 1500. We must find the total cost price (CP) of all sweets. All sweets are identical, so cost is proportional to quantity. Concept / Approach: Let the total cost price be x rupees. Then the cost of the first part is (3/5)x and the cost of the remaining part is (2/5)x. We calculate the selling price of each part by applying the respective profit or loss percentage. Adding these two selling prices gives the total selling price. The overall profit equals total selling price minus total cost price, which is given as Rs. 1500. This leads to an equation in x that we can solve to obtain the total cost price. Step-by-Step Solution: Step 1: Let total cost price be x rupees. Step 2: Cost of first part (3/5 of sweets) = (3/5)x. Step 3: Selling price of this part with 10% profit = (3/5)x * 1.10 = (3.3/5)x. Step 4: Cost of remaining part (2/5 of sweets) = (2/5)x. Step 5: Selling price of this part with 5% loss = (2/5)x * 0.95 = (1.9/5)x. Step 6: Total selling price = (3.3/5)x + (1.9/5)x = (5.2/5)x = 1.04x. Step 7: Overall profit = total SP - total CP = 1.04x - x = 0.04x. Step 8: Given overall profit = Rs. 1500, so 0.04x = 1500. Step 9: Therefore, x = 1500 / 0.04 = 1500 * 25 = Rs. 37,500. Verification / Alternative check: If total CP is Rs. 37,500, then CP of first part = (3/5) * 37,500 = 22,500. SP1 at 10% profit = 22,500 * 1.10 = 24,750. CP of second part = (2/5) * 37,500 = 15,000. SP2 at 5% loss = 15,000 * 0.95 = 14,250. Total SP = 24,750 + 14,250 = 39,000. Overall profit = 39,000 - 37,500 = Rs. 1,500, matching the given profit exactly. Why Other Options Are Wrong: Any other value for total cost such as Rs. 36,400, Rs. 37,415, Rs. 36,500, or Rs. 35,000 would lead to a different overall profit when the same percentages are applied. None of those values yield exactly Rs. 1,500 as the net gain, so they cannot be correct total cost prices under the given conditions. Common Pitfalls: Students sometimes wrongly average the profit and loss percentages as simple percentages without considering the fractions 3/5 and 2/5. Another mistake is to assume 10% and 5% apply to the same cost base or to forget that total profit is the difference between total selling price and total cost price. Always form equations based on money values, not just the percentages alone. Final Answer: The total cost price of all the sweets is Rs. 37,500.

Question 20

Anil purchases two books for a total of Rs. 100. He sells the first book at a loss of 5% and the second book at a profit of 20%. If his overall profit on the two books together is 5%, what is the cost price of the first book?

Accepted Answer

Introduction / Context: This question involves two items being sold at different profit and loss percentages, while an overall profit percentage on the combined transaction is specified. The task is to find the individual cost price of one item using total cost and total profit data. Such problems help candidates practise forming equations that balance total cost with total selling price and overall percentage profit. Given Data / Assumptions: Total cost price of two books = Rs. 100. First book is sold at a 5% loss. Second book is sold at a 20% profit. Overall profit on both books together = 5%. We need to find the cost price of the first book. Concept / Approach: Let the cost prices of the first and second books be C1 and C2 respectively. Then C1 + C2 = 100. We express the selling prices in terms of C1 and C2 using the given percentages: first at 95% of its cost and second at 120% of its cost. Overall profit of 5% means that the combined selling price equals 105% of the total cost price. This gives another equation. Solving the two equations together yields C1 and C2, from which we pick C1 as the required answer. Step-by-Step Solution: Step 1: Let cost price of first book = C1 and cost price of second book = C2. Step 2: Given C1 + C2 = 100. (Equation 1) Step 3: First book is sold at 5% loss, so SP1 = 0.95 * C1. Step 4: Second book is sold at 20% profit, so SP2 = 1.20 * C2. Step 5: Overall profit = 5%, so total SP = 1.05 * (C1 + C2) = 1.05 * 100 = 105. Step 6: Therefore, 0.95C1 + 1.20C2 = 105. (Equation 2) Step 7: From Equation 1, C2 = 100 - C1. Step 8: Substitute in Equation 2: 0.95C1 + 1.20(100 - C1) = 105. Step 9: Expand: 0.95C1 + 120 - 1.20C1 = 105. Step 10: Combine like terms: (0.95 - 1.20)C1 + 120 = 105 → (-0.25)C1 = -15. Step 11: Hence C1 = (-15) / (-0.25) = 60. Verification / Alternative check: If C1 = 60, then C2 = 40. SP1 at 5% loss = 0.95 * 60 = 57. SP2 at 20% profit = 1.20 * 40 = 48. Total SP = 57 + 48 = 105. Total CP = 100. Overall profit = 105 - 100 = 5, which is 5% of 100. This matches the required overall profit, confirming that the cost of the first book is Rs. 60. Why Other Options Are Wrong: Choosing 58, 55, 45 or 52 as the cost of the first book leads to a different pair of cost prices and ultimately a different overall profit percentage. None of these values produce exactly 5% overall profit when the given 5% loss and 20% gain are applied, so they are inconsistent with the conditions of the problem. Common Pitfalls: Learners sometimes assume both books have equal cost or try to average the percentages 5% and 20% directly. Another error is to take 5% of Rs. 100 and try to distribute it incorrectly between the two books without setting up proper equations. Writing clear equations for total cost and total selling price is the most reliable approach. Final Answer: The cost price of the first book is 60 rupees.

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