Question 1

A shopkeeper sells dried apricots at Rs 1310 per kilogram and incurs a loss of 13%. If he raises the selling price to Rs 1441 per kilogram, what will be his new percentage gain or loss?

Accepted Answer

Introduction / Context: This question is similar in structure to other profit and loss problems where a new selling price changes the magnitude of loss or profit. Initially, dried apricots are sold at a certain loss percent. After increasing the selling price, the shopkeeper still may have a loss, but usually a smaller one. The task is to compute the new percentage gain or loss after the price change, using the fact that cost price remains fixed. Given Data / Assumptions: Initial selling price SP1 = Rs 1310 per kg. Initial loss = 13%. New selling price SP2 = Rs 1441 per kg. We must determine whether SP2 leads to profit or loss, and its percentage. Cost price per kg is constant between both scenarios. Concept / Approach: We again use the loss formula to find cost price: Loss 13% means SP1 = 0.87 * CP. Thus CP = SP1 / 0.87. Compare SP2 with CP using percentage formula: (SP2 - CP) / CP * 100. A positive result gives profit; a negative result gives loss. Step-by-Step Solution: Step 1: Let cost price per kg = CP. Step 2: Loss of 13% implies SP1 = 0.87 * CP. Step 3: SP1 = 1310, so 1310 = 0.87 * CP. Step 4: CP = 1310 / 0.87. Step 5: Express 0.87 as 87 / 100, so CP = 1310 * 100 / 87 = 131000 / 87. Step 6: New selling price SP2 = 1441. Step 7: Profit or loss fraction = (SP2 - CP) / CP. Step 8: Compute SP2 - CP in fractional form: SP2 - CP = 1441 - 131000 / 87. Step 9: Convert 1441 to denominator 87: 1441 = 1441 * 87 / 87 = 125367 / 87. Step 10: Difference = (125367 - 131000) / 87 = -5633 / 87, which is negative, so it is a loss. Step 11: Loss fraction = (5633 / 87) / (131000 / 87) = 5633 / 131000 ≈ 0.043. Step 12: Loss percentage ≈ 0.043 * 100 = 4.3% loss. Verification / Alternative check: Approximate CP numerically: CP ≈ 1310 / 0.87 ≈ Rs 1505.75. Difference between CP and SP2 = 1505.75 - 1441 ≈ 64.75. Loss percentage ≈ 64.75 / 1505.75 * 100 ≈ 4.3%. This confirms that even with the increased selling price, the shopkeeper still faces a small loss of about 4.3% per kilogram. Why Other Options Are Wrong: 8.6 percent loss: This is larger than the computed loss and does not correspond to the new price. 4.3 percent gain: Incorrect because SP2 is still lower than CP, so a gain is impossible. 8.6 percent gain: Also impossible because a selling price below cost price can never create profit. Only 4.3 percent loss matches both exact fractional and approximate numerical calculations. Common Pitfalls: One frequent error is taking 1310 as cost price and computing profit directly from 1441. This ignores the initial loss percentage and leads to incorrect conclusions. Another mistake is to treat the 13% loss as being on the selling price instead of on cost price. Always remember: loss percentage is defined relative to cost price unless otherwise stated. Correctly reconstructing CP from SP1 is the key step. Final Answer: At the new selling price of Rs 1441 per kilogram, the shopkeeper incurs a 4.3 percent loss on dried apricots.

Question 2

A shopkeeper sells 22 pairs of Skechers shoes and earns a total profit equal to the selling price of 6 pairs of the same shoes. What is his profit percentage on each pair?

Accepted Answer

Introduction / Context: This question is about interpreting a verbal description of profit in terms of number of items sold. The shopkeeper's total profit from selling 22 pairs of shoes is equal to the selling price of 6 pairs. From this information, you must derive the profit percentage per pair. This style of question is common in profit and loss topics and emphasizes translation of words into algebraic equations. Given Data / Assumptions: Number of pairs sold = 22. Total profit from selling these 22 pairs equals the selling price of 6 pairs. Let SP be the selling price per pair. Let CP be the cost price per pair. We assume all pairs are identical and sold at the same price. Concept / Approach: We translate the condition into an equation: Total selling price for 22 pairs = 22 * SP. Total cost price for 22 pairs = 22 * CP. Total profit = 22 * SP - 22 * CP. Given: Total profit = selling price of 6 pairs = 6 * SP. We solve for the ratio SP / CP and then compute profit percentage = ((SP - CP) / CP) * 100. Step-by-Step Solution: Step 1: Let SP = selling price per pair, CP = cost price per pair. Step 2: Total SP for 22 pairs = 22 * SP. Step 3: Total CP for 22 pairs = 22 * CP. Step 4: Total profit = 22 * SP - 22 * CP. Step 5: Given condition: total profit = selling price of 6 pairs = 6 * SP. Step 6: So 22 * SP - 22 * CP = 6 * SP. Step 7: Rearrange: 22SP - 6SP = 22CP. Step 8: 16SP = 22CP. Step 9: Divide both sides by 16CP: SP / CP = 22 / 16 = 11 / 8. Step 10: Profit per pair = SP - CP = (11 / 8)CP - CP = (3 / 8)CP. Step 11: Profit percentage = (Profit / CP) * 100 = (3 / 8) * 100 = 37.5%. Verification / Alternative check: Assign a simple numerical CP, for example CP = Rs 8: Then SP = (11 / 8) * 8 = Rs 11. Profit per pair = 11 - 8 = Rs 3. Profit percentage = 3 / 8 * 100 = 37.5%. Total profit on 22 pairs = 22 * 3 = Rs 66. Selling price of 6 pairs = 6 * 11 = Rs 66. The total profit equals the selling price of 6 pairs, matching the given condition and confirming that the profit percentage is correct. Why Other Options Are Wrong: 27.2 percent, 54.4 percent, and 16.9 percent do not correspond to SP / CP = 11 / 8. If any of these percentages were used, the profit from 22 pairs would not exactly equal the selling price of 6 pairs. Only 37.5 percent yields the exact algebraic match to the problem statement. Common Pitfalls: A common mistake is to misinterpret the phrase "profit equal to the selling price of 6 pairs" as meaning the profit percentage is 6 / 22 of something, which is incorrect. Another error is to set equations based on per pair values incorrectly, forgetting to multiply by the number of pairs. Always translate the given condition into a precise mathematical equation using total cost and total selling price for all items sold. Final Answer: The shopkeeper's profit percentage on each pair of Skechers shoes is 37.5 percent.

Question 3

A vendor buys bananas at the rate of 2 for Re 1 and sells them at the rate of 10 for Rs 7. What is his overall profit or loss percentage on the bananas?

Accepted Answer

Introduction / Context: This question checks your understanding of unit cost and unit selling price when items are bought and sold in different group sizes. The vendor buys bananas in one ratio (2 for Re 1) and sells them in another ratio (10 for Rs 7). You need to convert both to a common per unit basis to find the profit or loss percentage. Such questions are classic in profit and loss sections of aptitude tests. Given Data / Assumptions: Buying rate: 2 bananas for Re 1. Selling rate: 10 bananas for Rs 7. We assume no wastage and that all bananas purchased are sold. We must find the profit or loss percentage. Concept / Approach: The easiest method is to find cost price and selling price per banana: CP per banana = total cost / number of bananas when buying. SP per banana = total selling price / number of bananas when selling. Then profit per banana = SP per banana - CP per banana. Profit percentage = (Profit / CP per banana) * 100. Since the numbers are small and simple, calculations are straightforward. Step-by-Step Solution: Step 1: Compute cost price per banana. Step 2: 2 bananas cost Re 1, so CP per banana = 1 / 2 = Rs 0.50. Step 3: Compute selling price per banana. Step 4: 10 bananas sell for Rs 7, so SP per banana = 7 / 10 = Rs 0.70. Step 5: Profit per banana = SP - CP = 0.70 - 0.50 = Rs 0.20. Step 6: Profit percentage = (0.20 / 0.50) * 100. Step 7: 0.20 / 0.50 = 0.4. Step 8: Profit percentage = 0.4 * 100 = 40%. Verification / Alternative check: Consider buying and selling the same number of bananas, for example 10 bananas: To buy 10 bananas at 2 for Re 1: for every 2 bananas, cost is Re 1, so 10 bananas cost 5 rupees. To sell 10 bananas at the given selling rate: 10 bananas sell for Rs 7. Profit on 10 bananas = 7 - 5 = Rs 2. Cost price of 10 bananas = Rs 5, profit percentage = 2 / 5 * 100 = 40%. This check confirms the same answer using a batch approach instead of per-unit calculations. Why Other Options Are Wrong: 40 percent loss: Incorrect because selling price per banana (Rs 0.70) is clearly higher than cost price (Rs 0.50). 28.57 percent gain: This percentage often comes from mixing up ratios, but does not match the computed profit ratio of 0.4. 28.5 percent loss: Also clearly wrong because there is a gain, not a loss. Only 40 percent gain matches both per unit and batch-based calculations exactly. Common Pitfalls: A common mistake is to compare the total buy and sell numbers directly without adjusting for quantity, for example comparing 2 for 1 with 10 for 7 in a confusing way. Always convert both rates to the same base, usually cost and selling price per single unit or for a common number of units like 10 or 20. Careless handling of decimal values like 0.5 and 0.7 can also cause errors, so work slowly and check your arithmetic. Final Answer: The vendor makes a 40 percent gain on the bananas.

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