Question 1

A street vendor buys bananas at a rate of 7 bananas for Rs 6 and sells them at a rate of 6 bananas for Rs 7. What is his overall percentage profit or loss?

Accepted Answer

Introduction / Context: This is a classic type of profit and loss question involving selling items by different count based rates instead of directly by unit price. The vendor buys bananas at one rate and sells them at another, and we must compute the percentage profit or loss. These problems are very common in competitive exams and require converting both buying and selling terms into per unit costs and then comparing them. Given Data / Assumptions: Purchase rate: 7 bananas for Rs 6. Selling rate: 6 bananas for Rs 7. All bananas are identical and there is no wastage. We need to find the overall percentage profit or loss. Concept / Approach: We calculate: Cost price per banana = total cost / number of bananas bought. Selling price per banana = total selling amount / number of bananas sold. Profit or loss per banana = selling price per banana minus cost price per banana. Profit percent = (profit per banana / cost price per banana) * 100. The same percentage will apply regardless of the total number sold due to linearity. Step-by-Step Solution: Cost for 7 bananas = Rs 6. Cost price per banana = 6 / 7 rupees. Selling price for 6 bananas = Rs 7. Selling price per banana = 7 / 6 rupees. Profit per banana = SP - CP = (7 / 6) - (6 / 7). Compute difference: (7 / 6) - (6 / 7) = (49 / 42) - (36 / 42) = 13 / 42. Cost price per banana = 6 / 7 = 36 / 42. Profit percent = (profit / cost) * 100 = (13 / 42) / (36 / 42) * 100. This simplifies to (13 / 36) * 100 ≈ 36.11%. Therefore, the vendor makes approximately 36.1% profit. Verification / Alternative check: Consider buying 42 bananas, a common multiple of 7 and 6: To get 42 bananas, the vendor buys 6 batches of 7 bananas. Total cost = 6 * 6 = Rs 36. He then sells 42 bananas in batches of 6 bananas each, that is 7 batches. Total revenue = 7 * 7 = Rs 49. Profit = 49 - 36 = Rs 13. Profit percent = (13 / 36) * 100 ≈ 36.11%. This matches the earlier calculation, confirming the answer. Why Other Options Are Wrong: Options claiming loss are impossible because the selling price per banana is clearly higher than the cost price per banana. A profit of 26.5% or 43.75% does not match the exact ratio of revenue to cost in this scheme. The accurate profit percent is about 36.1%, so the closest and correct option is 36.1% profit. Common Pitfalls: Many students mistakenly compare 7 and 6 directly without converting to per unit values. Others may invert the rate and treat 7 bananas for Rs 6 as Rs 7 for 6 bananas, leading to incorrect calculations. Always convert such rate problems to cost and selling price per single unit before computing percentages. Final Answer: The vendor makes a 36.1% profit on selling the bananas.

Question 2

A miner sells a diamond to a trader at a profit of 40%, and the trader then sells it to a customer at a further profit of 25%. If the customer pays Rs 56 lakhs for the diamond, what was the cost of the diamond to the miner (in lakhs)?

Accepted Answer

Introduction / Context: This problem involves successive profits made by different people in a chain of sales. The miner sells to the trader at one profit percentage, and then the trader sells to the final customer at another profit percentage. We are given the final selling price and must deduce the original cost to the miner. It tests understanding of compound percentage profit over multiple stages of resale. Given Data / Assumptions: Miner sells to trader at 40% profit. Trader sells to customer at 25% profit on his buying price. Customer pays Rs 56 lakhs. We denote the miner cost price by C lakhs. We need to determine C. Concept / Approach: Let C be the cost price for the miner: Trader's cost price = C * (1 + 40/100) = 1.4C. Customer's price (final selling price) = trader's cost * (1 + 25/100) = 1.4C * 1.25. Simplify 1.4 * 1.25 to find the overall multiplication factor from miner's cost to customer's payment. Then set that equal to 56 and solve for C. Step-by-Step Solution: Let miner cost price be C lakhs. Trader buys from miner at 40% profit, so trader cost price = 1.4C. Trader sells to customer at 25% profit, so final selling price = 1.25 * 1.4C. 1.25 * 1.4 = 1.75. Therefore customer price = 1.75C. Given that customer pays 56 lakhs, so 1.75C = 56. C = 56 / 1.75. C = 32 lakhs. Thus the diamond cost the miner Rs 32 lakhs. Verification / Alternative check: Verify by forward calculation: Miner cost price = 32 lakhs. Trader cost price = 32 * 1.4 = 44.8 lakhs. Customer price = 44.8 * 1.25 = 56 lakhs. These values exactly match the given final selling price. Also, miner profit = 44.8 - 32 = 12.8 lakhs, which is 40% of 32. Trader profit = 56 - 44.8 = 11.2 lakhs, which is 25% of 44.8. Everything is consistent, so C = 32 lakhs is correct. Why Other Options Are Wrong: If miner cost were 30 lakhs, trader cost would be 42 lakhs and final selling price 52.5 lakhs, not 56 lakhs. For 28 lakhs, final selling price would be 49 lakhs. For 25 lakhs, final selling price would be 43.75 lakhs. For 24 lakhs, final selling price would be 42 lakhs. None of these values match the customer payment of 56 lakhs. Common Pitfalls: Learners sometimes add profit percentages directly (40% + 25% = 65%) and treat the total multiplier as 1.65, which is incorrect because each percentage is applied to a different base. Another mistake is to treat 56 as profit instead of final selling price. Always work stepwise through each transaction and remember that successive percentages multiply, not simply add. Final Answer: The cost of the diamond to the miner was 32 lakhs.

Question 3

A grocer has 1600 kg of wheat. He sells part of it at a profit of 20% and the remaining part at a profit of 12%, so that his overall profit on the entire quantity is 17%. How many kilograms of wheat does he sell at 20% profit?

Accepted Answer

Introduction / Context: This question is another weighted average profit problem, similar to earlier rice and mango examples. The grocer sells some wheat at one profit rate and the rest at a different profit rate, but we know the overall profit percentage on the complete stock. Such questions assess a student's ability to set up and solve linear equations involving percentage profit and total quantities. Given Data / Assumptions: Total wheat = 1600 kg. Part sold at 20% profit. Remaining part sold at 12% profit. Overall profit on the entire 1600 kg is 17%. Cost price per kilogram is uniform. We must find the quantity sold at 20% profit. Concept / Approach: Let cost price per kg be C. If x kg is sold at 20% profit: Profit from x kg at 20% = 0.2Cx. Remaining quantity = 1600 - x kg, with profit 12%. Profit from (1600 - x) kg at 12% = 0.12C(1600 - x). Total profit = 0.17 * 1600C. Set up the equation for total profit using these profits, divide out C, and solve for x. Step-by-Step Solution: Let x be the quantity of wheat in kg sold at 20% profit. Then 1600 - x kg is sold at 12% profit. Assume cost price per kg is C. Total profit from x kg at 20% = 0.2Cx. Total profit from 1600 - x kg at 12% = 0.12C(1600 - x). Overall profit at 17% on all 1600 kg = 0.17 * 1600C. Equation: 0.2Cx + 0.12C(1600 - x) = 0.17 * 1600C. Divide both sides by C: 0.2x + 0.12(1600 - x) = 0.17 * 1600. 0.2x + 192 - 0.12x = 272. 0.08x = 80, hence x = 80 / 0.08 = 1000. So 1000 kg of wheat is sold at 20% profit. Verification / Alternative check: Verify with assumed cost price C = 1 per kg: 1000 kg at 20% gives profit 1000 * 0.2 = 200. 600 kg at 12% gives profit 600 * 0.12 = 72. Total profit = 200 + 72 = 272. Total cost = 1600 * 1 = 1600. Overall profit percent = (272 / 1600) * 100 = 17%. This confirms that the calculated distribution is correct. Why Other Options Are Wrong: If 600 kg were at 20% profit, the weighted profit would be much lower than 17%. Values like 800 kg or 1200 kg also lead to different overall profit percentages when computed carefully. Only 1000 kg at 20% and 600 kg at 12% produce exactly 17% overall profit. Common Pitfalls: A common mistake is to average 20% and 12% directly without considering quantities. Another error is to set up the profit equation incorrectly, mixing up which term corresponds to which quantity. Always represent the unknown quantity as a variable and write the total profit as the sum of profits from each part before equating it to the overall profit. Final Answer: The grocer sells 1000 kg of wheat at 20% profit.

Question 4

A shop offers a 60% discount on the marked price of an item, and after this discount the selling price becomes equal to the cost price. What was the percentage markup of the marked price over the cost price?

Accepted Answer

Introduction / Context: This question reverses the usual selling price calculation and asks about markup. The shopkeeper sets a marked price above the cost price and then gives a heavy discount. The special situation here is that, after a 60% discount, the final selling price exactly equals the cost price. We must determine how much higher the marked price was compared to the cost price. This is a straightforward percentage reasoning problem. Given Data / Assumptions: Let cost price be C. Marked price is unknown, call it M. Discount given on M is 60%. After discount, selling price equals cost price C. We need the percentage markup, that is (M - C) as a percentage of C. Concept / Approach: If the discount is 60%, then: Selling price SP = M * (1 - 60/100) = 0.4M. Given SP = C. Therefore 0.4M = C, so M = C / 0.4 = 2.5C. Markup percent = ((M - C) / C) * 100. Since M = 2.5C, markup = 1.5C, so markup percent = 150%. Step-by-Step Solution: Let cost price be C. Let marked price be M. A 60% discount on M means the customer pays 40% of M. Therefore selling price SP = 0.4M. Given that after discount SP = C. So 0.4M = C. M = C / 0.4 = 2.5C. Markup = M - C = 2.5C - C = 1.5C. Markup percentage = (1.5C / C) * 100 = 150%. Verification / Alternative check: Assume a convenient cost price, for example C = 100 rupees. Then marked price M = 2.5 * 100 = 250. Discount 60% on 250 gives discount = 150 rupees. Selling price = 250 - 150 = 100. The selling price equals the cost price, as required. Markup from 100 to 250 is 150%, which agrees with our calculation. Why Other Options Are Wrong: Markup of 100% would mean marked price is double the cost price. After 60% discount, the selling price would be 40% of 200, which is 80, not equal to the cost price. Markups of 250%, 40%, or 200% also lead to different selling prices after a 60% discount and do not match the condition that the selling price equals cost price. Only a 150% markup fits the given discount relation. Common Pitfalls: Learners sometimes treat discount on cost price instead of marked price or mix up markup percentage with discount percentage. Another frequent mistake is not converting the verbal relation "selling price becomes equal to cost price" into a simple equation. Always express selling price in terms of marked price and discount, then equate it to cost price when such conditions are mentioned. Final Answer: The marked price was increased by 150% over the cost price.

Question 5

A stall sells a pizza for Rs 200 and incurs a loss of 20%. At what price (in rupees) should the stall sell the same pizza in order to make a profit of 10%?

Accepted Answer

Introduction / Context: This is a straightforward profit and loss calculation involving two different selling situations for the same item. The stall first sells at a known loss percentage and we are asked to adjust the price so that a target profit percentage is achieved on the same cost price. This tests your ability to reverse engineer the cost price from a loss scenario and then compute a new selling price for a desired profit. Given Data / Assumptions: Pizza sold at Rs 200 gives a loss of 20%. Let cost price of the pizza be C. We want a selling price that yields a profit of 10% on the same cost price. We need this new selling price in rupees. Concept / Approach: We use: Loss of 20% means SP = 80% of CP, or SP = 0.8C. Given SP = 200, solve for C. Then for a profit of 10%, new SP = 110% of C, or SP = 1.1C. Calculate 1.1C with the cost price obtained. Step-by-Step Solution: Let cost price of the pizza be C. Loss of 20% means SP1 = 0.8C. Given SP1 = 200, so 0.8C = 200. C = 200 / 0.8. C = 250. For a profit of 10%, new selling price SP2 = 1.1C. SP2 = 1.1 * 250. SP2 = 275. Thus, the pizza must be sold for Rs 275 to earn a 10% profit. Verification / Alternative check: Check quickly with the cost price: Cost price C = 250. At SP = 200, loss = 250 - 200 = 50, loss percent = (50 / 250) * 100 = 20%. At SP = 275, profit = 275 - 250 = 25, profit percent = (25 / 250) * 100 = 10%. Both calculations are consistent with the conditions in the question, so our answer is correct. Why Other Options Are Wrong: Selling at 250 would only cover cost price with no profit or loss. Selling at 300 would give a profit of 20%, not 10%. Selling at 325 gives an even higher profit. Selling at 260 gives profit of only (260 - 250) / 250 * 100 = 4%, which is not equal to 10%. Therefore only Rs 275 gives exactly 10% profit. Common Pitfalls: Students sometimes treat the 20% loss incorrectly as 20% of selling price instead of cost price. Another error is to add 10% directly on the earlier selling price rather than the cost price. Always compute or infer the cost price first and then apply the desired profit percentage on that cost price to find the correct new selling price. Final Answer: The stall should sell the pizza for Rs 275 to make a 10% profit.

Question 6

A wholesaler has 200 dozens of mangoes. He sells some of these mangoes at a profit of 20% and the remaining mangoes at a profit of 10%, so that his overall profit on all the mangoes is 13%. How many dozens of mangoes does he sell at 20% profit?

Accepted Answer

Introduction / Context: This is a mixture or weighted average type question in the context of profit and loss. The wholesaler sells part of his stock at a higher profit percentage and the rest at a lower profit percentage, and the combined effect is given as an overall profit percentage. We are required to find how many dozens were sold at the higher rate of profit. This pattern is very frequent in aptitude exams. Given Data / Assumptions: Total stock = 200 dozens of mangoes. Some dozens sold at 20% profit. Remaining dozens sold at 10% profit. Overall profit on all mangoes = 13%. Cost price per dozen is uniform. We need the number of dozens sold at 20% profit. Concept / Approach: Assume cost price per dozen is C. Let x be the number of dozens sold at 20% profit: Profit from x dozens at 20% = 0.2Cx. Remaining dozens = 200 - x, profit on them = 0.1C(200 - x). Total profit on 200 dozens at 13% = 0.13 * 200C. We then set the total profit from both parts equal to the overall profit and solve for x. Step-by-Step Solution: Let x be the number of dozens sold at 20% profit. Then 200 - x dozens are sold at 10% profit. Assume cost price per dozen is C. Profit from x dozens at 20% = 0.2Cx. Profit from 200 - x dozens at 10% = 0.1C(200 - x). Total profit at 13% on all 200 dozens = 0.13 * 200C. Set up equation: 0.2Cx + 0.1C(200 - x) = 0.13 * 200C. Divide by C: 0.2x + 0.1(200 - x) = 0.13 * 200. 0.2x + 20 - 0.1x = 26. 0.1x = 6, so x = 60. Thus, 60 dozens are sold at 20% profit. Verification / Alternative check: Take cost price per dozen as 1 for simplicity: 60 dozens at 20% profit give profit = 60 * 0.2 = 12. 140 dozens at 10% profit give profit = 140 * 0.1 = 14. Total profit = 12 + 14 = 26. Total cost = 200 * 1 = 200. Overall profit percent = (26 / 200) * 100 = 13%. This matches the overall profit given in the question, so our solution is correct. Why Other Options Are Wrong: If 140 dozens were at 20%, the overall profit would be much higher than 13%. With 80, 120, or 100 dozens at 20%, the blended profit would differ from 13% when computed correctly. Only 60 dozens at 20% and 140 dozens at 10% give the required 13% overall profit on 200 dozens. Common Pitfalls: One common issue is to average 20% and 10% directly as 15% and then attempt to adjust without considering quantities. Another mistake is in forming the equation and putting the wrong coefficient on x or 200 - x. Always write the total profit as the sum of profits from both groups and equate it to the overall profit on the full 200 dozens. Final Answer: The wholesaler sells 60 dozens of mangoes at 20% profit.

Question 7

On a certain item, the initial profit is 120% of the cost price. If the cost price increases by 10% but the selling price remains the same, what will be the new profit percentage on the item?

Accepted Answer

Introduction / Context: This question involves profit percentage with a change in cost price but a fixed selling price. Initially, the profit on an item is 120% of its cost. Later the cost increases by 10%, but the selling price is not changed. We need to compute how this affects the profit percentage. This tests understanding of how profit percentages are sensitive to changes in cost price when selling price remains constant. Given Data / Assumptions: Initial profit = 120% of cost price. Let initial cost price be C. Initial profit = 1.2C, so selling price = C + 1.2C. Cost price increases by 10%, becoming 1.1C. Selling price stays the same as before. We must find the new profit percentage based on the new cost price. Concept / Approach: First compute the original selling price in terms of C: Original profit = 1.2C. Original selling price SP = C + 1.2C = 2.2C. When cost price increases by 10%: New cost price = 1.1C. Selling price remains 2.2C. New profit = SP - new CP = 2.2C - 1.1C = 1.1C. New profit percentage = (1.1C / 1.1C) * 100. Step-by-Step Solution: Let initial cost price be C. Initial profit is 120% of C, so profit = 1.2C. Therefore, original selling price SP = C + 1.2C = 2.2C. Cost price increases by 10%, so new cost price CP2 = 1.1C. Selling price remains SP = 2.2C. New profit = SP - CP2 = 2.2C - 1.1C. New profit = 1.1C. New profit percentage = (1.1C / 1.1C) * 100 = 100%. So the new profit percentage is 100%. Verification / Alternative check: Choose a convenient cost price, for example C = 100 rupees initially. Initial profit = 120% of 100 = 120 rupees. Initial selling price = 100 + 120 = 220 rupees. New cost price after 10% increase = 110 rupees. Selling price remains 220 rupees. New profit = 220 - 110 = 110 rupees. New profit percent = (110 / 110) * 100 = 100%. This simple numeric check confirms the algebraic solution. Why Other Options Are Wrong: Values like 50%, 60%, 90% or 75% do not arise from the given relations. Since the selling price is still much larger than the increased cost price, the profit percentage remains high. Specifically, the new profit is exactly equal to the new cost price, which implies a 100% profit, not any of the smaller percentages listed as distractors. Common Pitfalls: Many learners mistakenly treat the 120% as overall selling price rather than profit, or they add and subtract percentages without reference to the correct base. Another error is to compute the new profit percent still on the original cost price instead of the increased cost price. Always clearly define cost, selling price, and profit before and after the change, and be careful about which cost price you use when computing percentages. Final Answer: The new profit percentage on the item is 100%.

Question 8

A shopkeeper sells cocoa seeds at Rs 1330 per kg and incurs a loss of 15%. If he instead sells them at Rs 1463 per kg, what is his percentage profit or loss?

Accepted Answer

Introduction / Context: This question first gives a selling price at which the seller incurs a certain percentage loss and then changes the selling price. We are asked to determine the new profit or loss percentage at the new selling price. It is a good test of your ability to compute cost price from a given loss percentage and selling price, and then recompute profit or loss at a different selling price. Given Data / Assumptions: At a selling price of Rs 1330 per kg, the shopkeeper has a loss of 15%. Later he sells at Rs 1463 per kg. We assume the cost price per kg of cocoa seeds is constant. We need to find the new profit or loss percentage at Rs 1463 per kg. Concept / Approach: When there is a loss of 15%, selling price SP1 = 85% of cost price CP: SP1 = 0.85 * CP. Given SP1 = 1330, so CP can be obtained. Once CP is known, compute new profit or loss using SP2 = 1463. New profit or loss percentage = ((SP2 - CP) / CP) * 100. Step-by-Step Solution: Let cost price per kg be CP. Given: at SP1 = 1330, loss is 15%. Therefore SP1 = 0.85 * CP. So 0.85 * CP = 1330. CP = 1330 / 0.85. CP ≈ 1564.71 (rounded to two decimal places). Now selling price SP2 = 1463. Profit or loss per kg = SP2 - CP ≈ 1463 - 1564.71 = -101.71. The negative sign indicates a loss of about Rs 101.71 per kg. Loss percentage ≈ (101.71 / 1564.71) * 100 ≈ 6.5%. Thus, at Rs 1463 per kg, he still incurs about 6.5% loss. Verification / Alternative check: We can approximate CP for quick checking. If CP were exactly 1565, then 15% of 1565 is about 234.75, and SP1 would be about 1330.25, close to 1330 after rounding. At SP2 = 1463, the difference from CP of about 1565 is around 102, which is roughly 6.5% of 1565. This supports our more exact calculation that the new loss percent is about 6.5%. Why Other Options Are Wrong: 13% loss would mean the new selling price is even closer to the original loss case, which is not correct given the higher price. 6.5% gain would require SP2 to be above CP, but it is below CP. Likewise, 13% gain contradicts the loss situation. A 5% loss would require a selling price slightly closer to CP than 1463, so this option is also inaccurate. The correct approximate value is a 6.5% loss. Common Pitfalls: A common mistake is to assume that increasing the selling price from 1330 to 1463 automatically creates a profit, without first calculating the true cost price. Another error is to treat 15% as a fraction of the selling price rather than cost price. Always derive cost price accurately from the first scenario, then recompute any new profit or loss with respect to that same cost price. Final Answer: At the selling price of Rs 1463 per kg, the shopkeeper incurs approximately a 6.5% loss.

Question 9

A profit of Rs 7,28,000 has to be shared among three partners Amir, Balaraj and Charan in the ratio 7 : 5 : 4. How much money (in rupees) does Charan receive as his share of the profit?

Accepted Answer

Introduction / Context: This is a straightforward partnership and ratio distribution problem. When a total profit or amount is shared according to a given ratio, each partner’s share is determined by the proportion of their ratio part to the sum of all parts. Such questions are common in business mathematics and basic quantitative aptitude sections. Given Data / Assumptions: Total profit to be shared = Rs 7,28,000. Ratio of shares Amir : Balaraj : Charan = 7 : 5 : 4. We need Charan’s share of the profit. Concept / Approach: If a total T is divided in the ratio a : b : c, then: Total number of ratio parts = a + b + c. Each person’s share = (their ratio part / total ratio parts) * T. Here, Charan’s ratio part is 4 and the total ratio parts are 7 + 5 + 4. We use this to compute Charan’s share directly. Step-by-Step Solution: Total profit T = Rs 7,28,000. Ratio of shares: Amir : Balaraj : Charan = 7 : 5 : 4. Total ratio parts = 7 + 5 + 4 = 16. Charan’s ratio part = 4. Charan’s share = (4 / 16) * 7,28,000. 4 / 16 = 1 / 4. Charan’s share = (1 / 4) * 7,28,000. Charan’s share = 7,28,000 / 4 = 1,82,000. Therefore, Charan receives Rs 1,82,000. Verification / Alternative check: We can also compute shares of Amir and Balaraj to check: One ratio part = total profit / 16 = 7,28,000 / 16 = 45,500. Amir’s share = 7 * 45,500 = 3,18,500. Balaraj’s share = 5 * 45,500 = 2,27,500. Charan’s share = 4 * 45,500 = 1,82,000. Total = 3,18,500 + 2,27,500 + 1,82,000 = 7,28,000. The sum matches the total profit, so the distribution is correct. Why Other Options Are Wrong: Values like 2,27,500 or 3,18,500 belong to other partners. Rs 91,000 or 1,75,000 do not maintain the correct ratio when combined with other possible shares. Only Rs 1,82,000 is consistent with Charan’s ratio part of 4 out of 16 and sums correctly with the other partners’ shares to the total profit. Common Pitfalls: Some learners divide by 3 instead of the sum of the ratio parts or mistakenly assign the largest share to the smallest ratio. Others may compute parts correctly but miscalculate multiplication with the ratio numbers. Always sum the ratio components first, then calculate the value of one part, and finally multiply by each person’s ratio number to get individual shares. Final Answer: Charan receives Rs 1,82,000 as his share of the profit.

Question 10

A vendor buys bananas at a rate of 4 for Rs 3 and sells them at a rate of 3 for Rs 4. What is his overall percentage profit or loss?

Accepted Answer

Introduction / Context: This question is similar to other rate based profit and loss problems where items are bought and sold in groups rather than by direct unit price. The vendor purchases bananas at one grouped rate and sells them at another. We need to compute his overall percentage profit or loss. The key is to convert both rates into per unit prices and then compare them. Given Data / Assumptions: Buying rate: 4 bananas for Rs 3. Selling rate: 3 bananas for Rs 4. No bananas are wasted or spoiled. All bananas are identical. We must find the percentage profit or loss for the vendor. Concept / Approach: Compute: Cost price per banana = total cost / number of bananas in buying batch. Selling price per banana = total selling amount / number of bananas in selling batch. Then find profit per banana and divide by cost price per banana to get profit percent. The percentage result will be the same irrespective of total number of bananas sold due to proportionality. Step-by-Step Solution: Cost for 4 bananas = Rs 3. Cost price per banana = 3 / 4 rupees. Selling price for 3 bananas = Rs 4. Selling price per banana = 4 / 3 rupees. Profit per banana = SP - CP = (4 / 3) - (3 / 4). Compute difference: (4 / 3) - (3 / 4) = (16 / 12) - (9 / 12) = 7 / 12. Cost price per banana = 3 / 4 = 9 / 12. Profit percent = (profit / cost) * 100 = (7 / 12) / (9 / 12) * 100. This simplifies to (7 / 9) * 100 ≈ 77.78%. Thus, the vendor makes approximately 77.7% profit. Verification / Alternative check: Consider a convenient total such as 36 bananas, which is the least common multiple of 4 and 3: To buy 36 bananas, the vendor buys 9 batches of 4 bananas. Total cost = 9 * 3 = Rs 27. To sell 36 bananas, he sells 12 batches of 3 bananas. Total revenue = 12 * 4 = Rs 48. Profit = 48 - 27 = Rs 21. Profit percent = (21 / 27) * 100 = 77.78%. This confirms our earlier calculation. Why Other Options Are Wrong: 43.75% profit corresponds to a different buying and selling pattern, not this one. Any loss options are impossible because selling price per banana is clearly higher than the cost price per banana. Hence 77.7% loss and 43.75% loss are incorrect. The only option that matches the calculated 77.7% value is 77.7% profit. Common Pitfalls: Errors often come from reversing buying and selling rates or from incorrect fraction operations. Some students compare 4 and 3 directly without converting to a per unit basis. Others may mistakenly treat 4 for 3 and 3 for 4 as symmetric and assume no profit or loss. Always compute cost price per unit and selling price per unit first, then compare them. Final Answer: The vendor makes approximately a 77.7% profit on the bananas.

Question 11

For an article, the ratio of selling price to cost price is 13 : 17. What is the percentage loss incurred on the article?

Accepted Answer

Introduction / Context: This is a simple ratio based profit and loss question. Instead of giving actual numerical prices, the question provides the ratio of selling price to cost price, and we must determine whether there is a profit or loss and its percentage. Such questions test understanding of how to interpret price ratios and translate them into profit or loss percentages. Given Data / Assumptions: Ratio of selling price to cost price (SP : CP) is 13 : 17. This means SP / CP = 13 / 17. Since SP is less than CP, there is a loss. We need the loss percentage. Concept / Approach: Let cost price be CP and selling price be SP: SP / CP = 13 / 17. We can assume CP = 17 units and SP = 13 units for convenience. Loss = CP - SP = 17 - 13 = 4 units. Loss percent = (Loss / CP) * 100. This approach avoids actual rupee values and works entirely with the ratio numbers, which keeps the calculations simpler. Step-by-Step Solution: Given SP : CP = 13 : 17. Assume CP = 17 and SP = 13 (in the same units). Loss = CP - SP = 17 - 13 = 4. Loss percent = (Loss / CP) * 100. Loss percent = (4 / 17) * 100. Compute 4 / 17 ≈ 0.23529. Loss percent ≈ 0.23529 * 100 ≈ 23.529%. Rounded to two decimal places, this is approximately 23.52%. Verification / Alternative check: Take an actual numeric example with CP = Rs 17: Selling price SP = Rs 13. Loss = 17 - 13 = Rs 4. Loss percentage = (4 / 17) * 100 ≈ 23.529%. This is exactly the same as the ratio based calculation and shows that the result does not depend on the actual currency units chosen, only on the ratio of SP to CP. Why Other Options Are Wrong: A loss of 27.74%, 18.62%, 19.45% or 13.5% corresponds to different SP : CP ratios, not 13 : 17. Only 23.52% closely matches 4 / 17 * 100 and is therefore correct for the given ratio. Any other value would be mathematically inconsistent with SP / CP = 13 / 17. Common Pitfalls: Some learners mistakenly treat the ratio as CP : SP and compute profit instead of loss, or they use SP as the base when calculating percentage loss, which is incorrect since loss percent is always on cost price. Others reduce the ratio incorrectly or miscalculate the fraction 4 / 17. Always identify whether SP is greater or less than CP first and then use the correct base when computing percentages. Final Answer: The loss percentage on the article is approximately 23.52%.

Question 12

Puneet purchases 5 dozens of oranges at the rate of Rs 120 per dozen and sells every orange for Rs 11.50. What is his overall profit percentage on this transaction?

Accepted Answer

Introduction / Context: This problem is a straightforward profit and loss question involving buying oranges in dozens and selling them individually. It checks whether you can convert between dozens and single units, compute total cost price, total selling price, and then use the standard profit percentage formula. Such questions are very common in competitive exams and help you practice careful handling of units and percentages. Given Data / Assumptions: Puneet purchases 5 dozens of oranges. Cost price is Rs 120 per dozen. He sells each orange for Rs 11.50. We assume there is no wastage or spoilage; all oranges are sold. We need the overall profit percentage on the entire deal. Concept / Approach: The key ideas are: Convert dozens to number of oranges: 1 dozen = 12 oranges. Total cost price (CP) = number of dozens * price per dozen. Total selling price (SP) = number of oranges * selling price per orange. Profit = SP - CP. Profit percentage = (Profit / CP) * 100. Working systematically with totals instead of per unit simplifies the calculations and reduces mistakes. Step-by-Step Solution: Step 1: Compute total number of oranges = 5 dozens * 12 = 60 oranges. Step 2: Compute total cost price = 5 * 120 = Rs 600. Step 3: Compute total selling price = 60 * 11.50 = Rs 690. Step 4: Profit = SP - CP = 690 - 600 = Rs 90. Step 5: Profit percentage = (90 / 600) * 100. Step 6: (90 / 600) = 0.15, so profit percentage = 0.15 * 100 = 15%. Verification / Alternative check: We can also think in terms of per dozen profit. One dozen contains 12 oranges. At Rs 11.50 per orange, selling price per dozen is 12 * 11.50 = Rs 138. Cost price per dozen is Rs 120. So profit per dozen is Rs 18. Then profit percentage per dozen is (18 / 120) * 100 = 15%. Since all dozens are identical, the overall profit percentage remains 15%. This matches our earlier result, confirming the calculation is consistent. Why Other Options Are Wrong: 18%: This would require profit to be 18% of Rs 600, that is Rs 108, but actual profit is Rs 90 only. 30%: A 30% profit on Rs 600 would be Rs 180, which is much higher than the actual profit of Rs 90. 12%: A 12% profit would be (12 / 100) * 600 = Rs 72, which does not match the actual profit. Therefore, none of these values fit the correct profit computation, leaving 15% as the only valid answer. Common Pitfalls: Students sometimes forget to convert dozens to units and mistakenly multiply by 5 instead of 60 when computing selling price. Another common error is to mix up profit percentage on selling price versus cost price, but here the question clearly asks for profit percentage on cost price. Careless handling of the decimal 11.50 can also cause mistakes, so it is important to multiply carefully. Always recompute total cost and total selling price to avoid such errors. Final Answer: The overall profit percentage earned by Puneet on selling the oranges is 15%.

Question 13

A wholesaler sells a watch to a retailer at a profit of 20%, and the retailer then sells it to a customer at a loss of 10%. If the customer pays Rs 874.80 for the watch, what was the wholesaler's original cost price?

Accepted Answer

Introduction / Context: This question tests your understanding of successive profit and loss in a trade chain, where a wholesaler sells to a retailer and the retailer sells to a customer. You need to correctly apply percentage profit and percentage loss in reverse to find the original cost price of the wholesaler, given the final selling price to the customer. This is a standard type of profit and loss question used in many aptitude exams. Given Data / Assumptions: Let the wholesaler's cost price be Rs x. Wholesaler sells to retailer at a gain of 20%. Retailer sells to customer at a loss of 10%. Final selling price to the customer = Rs 874.80. We assume there are no other hidden costs such as tax, transport, or commission. Concept / Approach: The approach uses the relation between cost price and selling price with percentage changes: For profit p%, SP = CP * (1 + p / 100). For loss l%, SP = CP * (1 - l / 100). Here, the retailer's cost is the wholesaler's selling price. We work backward from the final selling price to find the wholesaler's cost price. By expressing everything in terms of x, we can set up a simple equation and solve it. Step-by-Step Solution: Step 1: Let wholesaler cost price = x. Step 2: Wholesaler gains 20%, so retailer cost price = x * (1 + 20 / 100) = 1.2x. Step 3: Retailer sells at a loss of 10%. So final selling price = 1.2x * (1 - 10 / 100) = 1.2x * 0.9 = 1.08x. Step 4: Given final selling price = Rs 874.80. So 1.08x = 874.80. Step 5: Solve for x: x = 874.80 / 1.08 = 810. Step 6: Therefore, the wholesaler's cost price was Rs 810. Verification / Alternative check: We can verify by moving forward through the trade chain: Wholesaler cost price = Rs 810. Wholesaler sells at 20% profit: 20% of 810 = 0.2 * 810 = 162. So wholesaler selling price = 810 + 162 = Rs 972. Retailer cost price = Rs 972. Retailer sells at 10% loss: 10% of 972 = 97.20. So final selling price = 972 - 97.20 = Rs 874.80. This matches the given customer payment exactly, so the calculation and the value of x are correct. Why Other Options Are Wrong: Rs 945: If this were the wholesaler cost, the final selling price would not match 874.80 after applying the given percentages. Rs 994 and Rs 675: Similar checks with profit and loss formulas show that these starting values do not lead to a final price of Rs 874.80. Thus, only Rs 810 produces the correct final customer price and satisfies all conditions. Common Pitfalls: A very common mistake is to add or subtract percentages directly instead of applying them multiplicatively. Another frequent error is to treat both 20% and 10% as profits or to ignore that the second transaction is a loss. Some students also incorrectly assume that the total percentage change is 20% minus 10% = 10% profit, which is not valid here because the percentages are taken on different bases. Always carefully track which price each percentage applies to. Final Answer: The wholesaler originally paid Rs 810 for the watch.

Question 14

A merchant offers a discount of 25% on the list price of an item and then incurs a loss of 5%. What percentage profit or loss will the merchant make if instead the item is sold at a discount of only 10% on the same list price?

Accepted Answer

Introduction / Context: This question combines discount and profit or loss concepts. The key idea is that discount is applied on the list (marked) price, while profit or loss is always calculated on the cost price. You are given one selling scenario that leads to loss and are asked to find the percentage profit or loss in a different discount scenario using the same list price. This type of question appears frequently in aptitude tests to check conceptual clarity on pricing structures. Given Data / Assumptions: Let the list price be L. First case: discount = 25%, so selling price SP1 = 0.75L. Under SP1, the merchant has a loss of 5%. Second case: discount = 10%, so selling price SP2 = 0.90L. We must find the profit or loss percentage in the second case. No taxes, extra costs, or hidden charges are mentioned. Concept / Approach: The steps are: Use the first scenario to relate cost price (CP) and list price L. Loss of 5% means SP1 = 0.95 * CP. Equate 0.75L = 0.95 * CP to find CP in terms of L. Use this CP and SP2 = 0.90L to compute profit percentage in the second scenario. The key formula is profit percentage = ((SP - CP) / CP) * 100. Step-by-Step Solution: Step 1: From first case, SP1 = 0.75L. Step 2: Loss of 5% means SP1 = 0.95 * CP. Step 3: So 0.75L = 0.95 * CP, hence CP = 0.75L / 0.95. Step 4: In the second case, SP2 = 0.90L (10% discount on list price). Step 5: Profit percentage in second case = ((SP2 - CP) / CP) * 100. Step 6: Substitute CP: SP2 - CP = 0.90L - (0.75L / 0.95). Step 7: Compute CP in fraction form: CP = (75 / 95)L = (15 / 19)L. Step 8: SP2 = 0.90L = (9 / 10)L. Step 9: Profit fraction = ((9 / 10)L - (15 / 19)L) / ((15 / 19)L). Step 10: Simplify numerator: (9 / 10 - 15 / 19)L = ((171 - 150) / 190)L = (21 / 190)L. Step 11: Divide by CP: (21 / 190)L / ((15 / 19)L) = (21 / 190) * (19 / 15) = 1 / 7. Step 12: Profit percentage = (1 / 7) * 100 ≈ 14% profit. Verification / Alternative check: Take a convenient value for L, for example L = Rs 190. Then: SP1 = 0.75 * 190 = Rs 142.50. Since SP1 is at 5% loss, CP = SP1 / 0.95 = 142.50 / 0.95 = Rs 150. In the second case, SP2 = 0.90 * 190 = Rs 171. Profit = SP2 - CP = 171 - 150 = Rs 21. Profit percentage = 21 / 150 * 100 = 14%. This numerical check fully confirms the symbolic calculation. Why Other Options Are Wrong: 5.5 percent loss: This would imply SP2 is less than CP, which contradicts our calculation that SP2 is higher. 50 percent profit: This would require much larger difference between SP2 and CP than observed. 26 percent loss: Also inconsistent because SP2 is clearly above CP once numbers are plugged in. Therefore, these values do not satisfy the relationship between list price, discounts, and cost price derived from the first scenario. Common Pitfalls: A frequent mistake is to treat discount percentage and loss percentage as directly comparable and to attempt adding or subtracting them without considering bases. Another error is to assume CP equals the list price, which is not stated. Some students may also incorrectly use SP1 as CP for the second case. The correct approach is always to find CP from one scenario, then use that CP to analyze any new selling arrangement. Final Answer: If the item is sold at a 10% discount on the list price, the merchant makes a 14 percent profit.

Question 15

A trader has 9 quintals of wheat. He sells part of it at a profit of 10% and the rest at a profit of 20%, resulting in an overall profit of 14%. How many kilograms of wheat are sold at 20% profit?

Accepted Answer

Introduction / Context: This problem involves a mixture of two different profit percentages applied to different portions of the same commodity. It tests your ability to use weighted averages or alligation concepts on profit percentages. The total quantity and the overall profit percentage are given, and you must work backwards to find how much quantity was sold at the higher profit rate. Given Data / Assumptions: Total wheat = 9 quintals. 1 quintal = 100 kg, so total quantity = 900 kg. Part is sold at 10% profit. Remaining part is sold at 20% profit. Overall profit percentage on the entire 9 quintals is 14%. We need the quantity (in kg) sold at 20% profit. Concept / Approach: We use a weighted average of profit percentages: Let x quintals be sold at 20% profit. Then (9 - x) quintals are sold at 10% profit. Overall profit percentage = (Total profit) / (Total cost) * 100. Since total cost is proportional to total quantity, we can equate the weighted average of percentages directly. Thus, we set up an equation based on the average of 10% and 20% giving 14% over the whole 9 quintals. Step-by-Step Solution: Step 1: Let x quintals be sold at 20% profit. Step 2: Then 9 - x quintals are sold at 10% profit. Step 3: Total profit (in percentage terms) on 9 quintals is given as 14%. Step 4: Weighted average equation: (10 * (9 - x) + 20 * x) / 9 = 14. Step 5: Simplify numerator: 10 * (9 - x) + 20 * x = 90 - 10x + 20x = 90 + 10x. Step 6: So (90 + 10x) / 9 = 14. Step 7: Multiply both sides by 9: 90 + 10x = 126. Step 8: 10x = 126 - 90 = 36, so x = 36 / 10 = 3.6 quintals. Step 9: Convert to kilograms: 3.6 quintals * 100 kg per quintal = 360 kg. Verification / Alternative check: Assume cost price per kg is Rs 1 to simplify: Total cost = 900 kg * 1 = Rs 900. Quantity at 20% profit = 360 kg, so profit there = 0.20 * 360 = Rs 72. Quantity at 10% profit = 900 - 360 = 540 kg, so profit there = 0.10 * 540 = Rs 54. Total profit = 72 + 54 = Rs 126. Overall profit percentage = 126 / 900 * 100 = 14%. This matches the given overall profit percentage, confirming that the quantity at 20% profit is indeed 360 kg. Why Other Options Are Wrong: 540 kg: If this much were sold at 20% profit, the weighted average profit would be higher than 14%. 180 kg: This would make the average profit less than 14% because most wheat would earn only 10%. 720 kg: This would heavily favor the 20% side, leading to a much larger overall profit percentage. Only 360 kg satisfies the overall 14% profit condition. Common Pitfalls: Students sometimes confuse the units, forgetting to convert quintals to kilograms or vice versa. Others incorrectly average the percentages as (10 + 20) / 2 = 15% without considering quantity distribution, which is wrong here because different quantities are sold at different rates. It is crucial to use the weighted average formula based on quantities, not just average the percentages blindly. Final Answer: The trader sells 360 kg of wheat at a 20% profit.

Question 16

A merchant offers a discount of 10% on the list price of an item and incurs a loss of 25%. If instead the item is sold at a discount of 20% on the same list price, what percentage profit or loss will the merchant make?

Accepted Answer

Introduction / Context: Here we again relate discount on list price with profit or loss on cost price. The question describes two different discount scenarios on the same list price and specifies that the merchant makes a loss of 25% in the first case. You are asked to determine the profit or loss percentage in the second case. This type of problem checks whether you can consistently track the relationship between list price, cost price, and selling price. Given Data / Assumptions: Let the list price be L. First case: discount = 10%; selling price SP1 = 0.90L. Under SP1, there is a loss of 25%. Second case: discount = 20%; selling price SP2 = 0.80L. We need the profit or loss percentage in the second scenario. No extra costs, commissions, or taxes are involved. Concept / Approach: We use: Loss of 25% implies SP1 = 0.75 * CP. We know SP1 in terms of L, so 0.90L = 0.75 * CP. From this, we find CP in terms of L. Then we compare SP2 = 0.80L with CP to compute the new profit or loss percentage. The formula remains profit or loss percentage = ((SP - CP) / CP) * 100 (positive for profit, negative for loss). Step-by-Step Solution: Step 1: First case SP1 = 0.90L (10% discount). Step 2: Loss of 25% means SP1 = 0.75 * CP. Step 3: Equate 0.90L = 0.75 * CP. Step 4: Solve for CP: CP = 0.90L / 0.75 = 1.20L. Step 5: Second case SP2 = 0.80L (20% discount). Step 6: Profit or loss fraction = (SP2 - CP) / CP = (0.80L - 1.20L) / 1.20L. Step 7: Simplify numerator: 0.80L - 1.20L = -0.40L. Step 8: So fraction = (-0.40L) / 1.20L = -1 / 3. Step 9: Percentage loss = (1 / 3) * 100 ≈ 33.33% loss. Verification / Alternative check: Let L = Rs 300 for easier numbers: First case: SP1 = 0.90 * 300 = Rs 270. Given 25% loss, CP = SP1 / 0.75 = 270 / 0.75 = Rs 360. Second case: SP2 = 0.80 * 300 = Rs 240. Loss = CP - SP2 = 360 - 240 = Rs 120. Loss percentage = 120 / 360 * 100 = 33.33% loss. This numerical example agrees exactly with the algebraic solution and confirms that the loss is about one third of the cost price. Why Other Options Are Wrong: 5 percent profit: Incorrect because SP2 is less than CP, so there cannot be any profit. 90 percent profit: This would require SP2 to be almost double CP, which is impossible here because SP2 is lower than CP. 20 percent profit: Again implies SP2 greater than CP, which conflicts with the computed values. Only an approximate 33.33 percent loss matches the relationship between list price, cost price, and new selling price. Common Pitfalls: Learners sometimes assume CP is equal to the list price, which is never stated in the question. Another mistake is adding or subtracting percentages directly (for example, treating 10% discount and 25% loss as related linearly). It is essential to build equations based on how each percentage applies to either the list price or cost price, and then solve logically instead of relying on intuition alone. Final Answer: When the item is sold at a 20% discount on the list price, the merchant incurs a 33.33 percent loss.

Question 17

When a sweater is sold with a 20% discount on its marked price, the shopkeeper still makes a profit of 28%. If the discount is reduced to 14% on the same marked price, what will be the new profit percentage?

Accepted Answer

Introduction / Context: This is another profit and loss question involving a change in discount while the marked price remains the same. The idea is to deduce the cost price from one scenario where both discount and profit are known, and then use that cost price to compute profit in a second scenario with a different discount. These questions sharpen your understanding of how discount percentages on marked price relate to profit percentages on cost price. Given Data / Assumptions: Let the marked (list) price be M. First case: discount = 20%, so SP1 = 0.80M. Under SP1, profit = 28%, so SP1 = 1.28 * CP. Second case: discount = 14%, so SP2 = 0.86M. We need the new profit percentage in the second case. All other factors like taxes and costs are assumed unchanged. Concept / Approach: Method: Use 0.80M = 1.28 * CP to find CP in terms of M. Then compare SP2 = 0.86M with CP to compute profit percentage. Profit percentage = ((SP2 - CP) / CP) * 100. The key is that CP is fixed while the marked price and discount determine different selling prices. Step-by-Step Solution: Step 1: From first case, SP1 = 0.80M. Step 2: Profit of 28% implies SP1 = 1.28 * CP. Step 3: So 0.80M = 1.28 * CP, hence CP = 0.80M / 1.28. Step 4: Simplify CP: CP = (80 / 128)M = (5 / 8)M = 0.625M. Step 5: In second case, SP2 = 0.86M (14% discount). Step 6: Profit fraction = (SP2 - CP) / CP = (0.86M - 0.625M) / 0.625M. Step 7: Numerator = 0.235M, denominator = 0.625M. Step 8: Profit fraction = 0.235 / 0.625 = 0.376. Step 9: Profit percentage = 0.376 * 100 = 37.6%. Verification / Alternative check: Take an easy value for the marked price, say M = Rs 1000: First case: SP1 = 0.80 * 1000 = Rs 800. Profit 28% means CP = SP1 / 1.28 = 800 / 1.28 = Rs 625. Second case: SP2 = 0.86 * 1000 = Rs 860. Profit = SP2 - CP = 860 - 625 = Rs 235. Profit percentage = 235 / 625 * 100 = 37.6%. The numerical check confirms the algebraic calculation and removes any ambiguity. Why Other Options Are Wrong: 42 percent, 46.4 percent, and 33.2 percent all come from incorrect handling of the relationship between discount and profit. They might arise if someone mistakenly treats profit percentages directly in relation to the marked price or confuses SP1 and SP2 in calculations. None of these values exactly match the correct ratio between SP2 and CP, which we have verified carefully. Common Pitfalls: A common mistake is assuming that reducing the discount by a certain percentage automatically increases profit by the same percentage, which is incorrect. Another error is treating the 28% profit as being on the marked price rather than on cost price. You must always be clear about which base each percentage is applied to: discount on marked price, profit or loss on cost price. Keeping this distinction straight is essential for accuracy. Final Answer: With a 14% discount on the marked price, the shopkeeper earns a 37.6 percent profit on the sweater.

Question 18

A wholesaler sells a watch to a retailer at a profit of 25%, and the retailer then sells it to a customer at a loss of 12%. If the customer pays Rs 1045 for the watch, what was the wholesaler's original cost price?

Accepted Answer

Introduction / Context: This problem involves two successive transactions of the same product. The wholesaler first sells to the retailer at a profit, and the retailer then sells to the final customer at a loss. You are given the final selling price and must work backwards to find the wholesaler's original cost price. Understanding how sequential profit and loss percentages combine is crucial for such questions. Given Data / Assumptions: Let wholesaler cost price be Rs x. Wholesaler profit = 25%; his selling price to retailer = 1.25x. Retailer incurs a loss of 12% on his purchase price. Final selling price to customer = Rs 1045. No other costs or taxes are involved. Concept / Approach: Since the retailer's cost price is the wholesaler's selling price, we proceed as follows: Retailer cost price = 1.25x. Loss of 12% means final SP = 0.88 * retailer cost price. So final SP = 0.88 * 1.25x. Set this equal to Rs 1045 and solve for x. The multiplication of 1.25 and 0.88 gives the combined effect on the wholesaler's cost price. Step-by-Step Solution: Step 1: Let wholesaler CP = x. Step 2: Wholesaler sells at a profit of 25%, so his SP = 1.25x. Step 3: Retailer buys at 1.25x and sells at a loss of 12%. Step 4: Retailer SP to customer = 1.25x * (1 - 12 / 100) = 1.25x * 0.88. Step 5: Compute the product: 1.25 * 0.88 = 1.10. Step 6: So final SP = 1.10x = Rs 1045. Step 7: Solve for x: x = 1045 / 1.10 = 950. Step 8: Therefore, the wholesaler's original cost price was Rs 950. Verification / Alternative check: Work forward from CP = Rs 950: Wholesaler sells at 25% profit: 25% of 950 = 0.25 * 950 = Rs 237.50. Wholesaler SP = 950 + 237.50 = Rs 1187.50. Retailer cost price = Rs 1187.50. Retailer sells at 12% loss: 12% of 1187.50 = 0.12 * 1187.50 = Rs 142.50. Final SP = 1187.50 - 142.50 = Rs 1045. The final price matches the given amount paid by the customer, confirming that the wholesaler cost price is correct. Why Other Options Are Wrong: Rs 1149, Rs 1244, and Rs 751 all fail when you apply the sequence of 25% profit followed by 12% loss. None of them yields a final selling price of exactly Rs 1045. Only Rs 950, when processed through both steps, gives the correct final value, so it is the unique correct answer. Common Pitfalls: Some learners mistakenly add or subtract percentages (for example, 25% profit and 12% loss gives net 13% profit), which is incorrect because they are applied on different bases. Others might try to treat Rs 1045 as being 12% below a certain value without accounting for the earlier 25% profit. Always relate each percentage to the correct cost or selling price at that stage of the transaction chain. Final Answer: The wholesaler originally purchased the watch for Rs 950.

Question 19

A shopkeeper sells cashew nuts at Rs 1260 per kilogram and incurs a loss of 8%. If he decides to sell at Rs 1386 per kilogram instead, what will be his new percentage gain or loss?

Accepted Answer

Introduction / Context: This problem focuses on changing the selling price of a commodity and observing how the profit or loss percentage changes while the cost price remains fixed. Initially, cashew nuts are sold at a loss, but after increasing the selling price, the shopkeeper may move into a small profit. The question tests your ability to find cost price from a known loss situation and then recompute the new profit percentage with a different selling price. Given Data / Assumptions: Initial selling price SP1 = Rs 1260 per kg. Initial transaction gives a loss of 8%. New selling price SP2 = Rs 1386 per kg. We need the new profit or loss percentage. The cost price per kg remains constant between the two situations. Concept / Approach: Use loss formula to find cost price: Loss 8% means SP1 = 0.92 * CP. From SP1, compute CP = SP1 / 0.92. Then compare SP2 with CP using profit or loss percentage = ((SP2 - CP) / CP) * 100. This sequence shows how a change in selling price can flip loss into gain. Step-by-Step Solution: Step 1: Let cost price per kg = CP. Step 2: Loss of 8% means SP1 = 0.92 * CP. Step 3: We know SP1 = 1260, so 1260 = 0.92 * CP. Step 4: CP = 1260 / 0.92. Step 5: Compute using fraction form: 0.92 = 92 / 100, so CP = 1260 * 100 / 92 = 126000 / 92 = 31500 / 23. Step 6: New selling price SP2 = 1386. Step 7: Profit or loss fraction = (SP2 - CP) / CP = (1386 - CP) / CP. Step 8: Use CP = 31500 / 23. Then SP2 - CP = 1386 - 31500 / 23 = (1386 * 23 - 31500) / 23 = (31878 - 31500) / 23 = 378 / 23. Step 9: Profit fraction = (378 / 23) / (31500 / 23) = 378 / 31500 = 63 / 5250 = 1 / 83.333... Step 10: Profit percentage ≈ (1 / 83.333...) * 100 = 1.2% gain. Verification / Alternative check: Approximate CP numerically: CP ≈ 1260 / 0.92 ≈ Rs 1369.565. Difference between new SP and CP = 1386 - 1369.565 ≈ 16.435. Profit percentage ≈ 16.435 / 1369.565 * 100 ≈ 1.20%. This confirms a small positive profit of around 1.2%, consistent with the exact fractional calculation, so the new selling price yields a modest gain. Why Other Options Are Wrong: 2.4 percent gain: This would require the difference between SP2 and CP to be roughly double what we computed. 1.2 percent loss: Incorrect because SP2 is actually slightly higher than CP, not lower. 2.4 percent loss: Also impossible since a higher selling price than cost price cannot produce a loss. Only 1.2 percent gain matches both exact and approximate calculations. Common Pitfalls: Some students invert the formula and compute CP as 0.92 * 1260, which is wrong because loss percentage is given on CP, not on SP. Others may accidentally treat 1260 as CP and directly compute profit with the new SP, ignoring that the initial situation involved a loss. Always reconstruct CP correctly from the given loss information before re-evaluating profit or loss at a new selling price. Final Answer: When the selling price is increased to Rs 1386 per kilogram, the shopkeeper makes a 1.2 percent gain on cashew nuts.

Question 20

The line passing through the point (-3, 1) and the point (x, 5) is parallel to the line passing through the points (-2, -1) and (6, 3). What is the value of x?

Accepted Answer

Introduction / Context: This is a coordinate geometry question about slopes of lines. Two lines are parallel if and only if they have the same slope. You are given two points on one line and one known point plus one variable x coordinate on the other line. By equating slopes, you can solve for x. This type of question is common in algebra and analytic geometry sections of aptitude and entrance exams. Given Data / Assumptions: First line passes through points A(-3, 1) and B(x, 5). Second line passes through points C(-2, -1) and D(6, 3). The two lines are parallel. We assume standard Cartesian coordinates and the usual definition of slope. Concept / Approach: The slope m of a line through points (x1, y1) and (x2, y2) is: m = (y2 - y1) / (x2 - x1). For two lines to be parallel: Their slopes must be equal, provided both are non-vertical. So slope of AB = slope of CD. We will compute the slope of CD first since both its coordinates are fully known, and then equate it to the slope of AB to solve for x. Step-by-Step Solution: Step 1: Compute slope of line CD through points C(-2, -1) and D(6, 3). Step 2: Slope m_CD = (3 - (-1)) / (6 - (-2)) = (3 + 1) / (6 + 2) = 4 / 8 = 1 / 2. Step 3: Compute slope of line AB through points A(-3, 1) and B(x, 5). Step 4: Slope m_AB = (5 - 1) / (x - (-3)) = 4 / (x + 3). Step 5: Since the lines are parallel, set slopes equal: 4 / (x + 3) = 1 / 2. Step 6: Cross multiply: 4 * 2 = 1 * (x + 3). Step 7: So 8 = x + 3. Step 8: Solve for x: x = 8 - 3 = 5. Verification / Alternative check: Now that we have x = 5, recompute the slope of AB to confirm: Point B becomes (5, 5). Slope m_AB = (5 - 1) / (5 - (-3)) = 4 / 8 = 1 / 2. This equals the slope of CD, which we already found to be 1 / 2. Since both slopes are identical and finite, the two lines are indeed parallel for x = 5. No other value of x satisfies this equality, so the solution is unique. Why Other Options Are Wrong: If x = -5, slope m_AB = 4 / (-5 + 3) = 4 / (-2) = -2, which does not equal 1 / 2. If x = -2, slope m_AB = 4 / (1) = 4, again not equal to 1 / 2. If x = 2, slope m_AB = 4 / (5) = 0.8, still not equal to 1 / 2. Therefore, only x = 5 makes the slopes equal and the lines parallel. Common Pitfalls: Students sometimes reverse the order of subtraction in the slope formula and thereby introduce sign errors. Another common mistake is to confuse the condition for perpendicular lines (product of slopes equal to -1) with the condition for parallel lines (slopes equal). It is also important to handle negative coordinates carefully when adding or subtracting. Always rewrite expressions like x - (-3) as x + 3 explicitly to avoid sign mistakes. Final Answer: The value of x that makes the two lines parallel is 5.

Profit and Loss Questions