Question 1

Karthik incurs a loss of 40% when he sells an article for Rs. 5,640. At what price should he have sold the article in order to make a profit of 25% on the cost price?

Accepted Answer

Introduction / Context: Here we move from a known loss situation to a desired profit situation on the same article. The selling price that produced a loss is given, and we are asked what selling price would produce a specified gain. This problem reinforces the connection between cost price, loss percentage and profit percentage, and how we can move from one scenario to another by recalculating the selling price relative to the cost price. Given Data / Assumptions: Selling price with loss = Rs. 5,640. Loss at this selling price = 40% of cost price. Required new selling price should give a profit of 25% on the same cost price. Cost price is assumed constant in both situations. No additional expenses or changes in quantity are involved. Concept / Approach: A 40% loss means the selling price equals 60% of cost price. Using SP = 0.60 * CP and SP = 5,640, we can find CP. Then, a 25% profit corresponds to a selling price equal to 125% of cost price. We compute this as SP = 1.25 * CP. The sequence is: derive cost price from a known loss scenario and then apply the desired profit percentage to that cost price to determine the required new selling price. Step-by-Step Solution: Step 1: Let cost price = CP. Step 2: Given a loss of 40%, selling price SP1 = 0.60 * CP. Step 3: We know SP1 = Rs. 5,640, so 0.60 * CP = 5,640. Step 4: Therefore, CP = 5,640 / 0.60. Step 5: Compute CP: 5,640 / 0.60 = 5,640 * (10 / 6) = 5,640 * (5 / 3) = 9,400. Step 6: For a profit of 25%, required selling price SP2 = 1.25 * CP. Step 7: SP2 = 1.25 * 9,400 = 9,400 * (5 / 4) = 11,750. Step 8: Thus, the article should be sold at Rs. 11,750 to get a 25% profit. Verification / Alternative check: Check both scenarios explicitly. For CP = Rs. 9,400 and SP1 = Rs. 5,640, loss = 9,400 - 5,640 = 3,760. Loss percentage = (3,760 / 9,400) * 100 = 40%. For SP2 = Rs. 11,750, profit = 11,750 - 9,400 = 2,350. Profit percentage = (2,350 / 9,400) * 100 = 25%. Both checks confirm the correctness of the cost price and the required selling price. Why Other Options Are Wrong: Selling prices such as Rs. 12,550, Rs. 13,650 or Rs. 11,550 would produce profit percentages different from 25% when calculated with CP = Rs. 9,400. The option Rs. 10,750 results in a profit that is too small. Only Rs. 11,750 corresponds exactly to a 25% profit on the cost price derived from the given loss condition. Common Pitfalls: Some learners might incorrectly assume that the increase from the loss selling price to the profit selling price is a simple percentage of the initial SP rather than recalculating from cost price. Others may misinterpret 40% loss as meaning SP is 40% of CP instead of 60% of CP. Carefully writing the equations SP = (1 - loss%) * CP and SP = (1 + profit%) * CP avoids these misunderstandings. Final Answer: Karthik should have sold the article for Rs. 11,750 to earn a 25% profit.

Question 2

The selling price of a mat is five times the discount offered on it. If the percentage discount is equal to the percentage profit, what is the ratio of the discount offered to the cost price of the mat?

Accepted Answer

Introduction / Context: This is an algebraic profit and discount question involving a relationship between selling price, discount and profit percentages. The condition that the selling price is a multiple of the discount amount, together with the equality of discount percentage and profit percentage, creates equations that link the cost price, marked price and discount. The task is to find the ratio of the discount amount to the cost price of the mat, which is a common type of ratio based question in aptitude exams. Given Data / Assumptions: Selling price (SP) is five times the discount (D), so SP = 5D. Let marked price (MP) be M. Discount amount D = M - SP. Discount percentage = (D / M) * 100. Profit percentage = (SP - CP) / CP * 100, where CP is cost price. Given that discount percentage equals profit percentage. We must find the ratio of discount amount D to cost price CP, that is D : CP. Concept / Approach: We first express SP in terms of D and then relate M to D using the definition of discount amount. From SP = 5D and D = M - SP, we get M = 6D. Discount percentage becomes (D / 6D) * 100 = (1/6) * 100. Since profit percentage must equal this value, we equate (SP - CP) / CP to 1/6 in fractional form. With SP expressed as 5D, we obtain a linear equation linking D and CP. Simplifying that equation gives the desired ratio D : CP. Step-by-Step Solution: Step 1: Let discount amount be D and marked price be M. Step 2: Given SP = 5D. Step 3: By definition of discount, D = M - SP = M - 5D, so M = 5D + D = 6D. Step 4: Discount percentage = (D / M) * 100 = (D / 6D) * 100 = (1/6) * 100. Step 5: So discount percent = profit percent = 1/6 in fractional form. Step 6: Let cost price be CP. Step 7: Profit percent = (SP - CP) / CP = 1/6. Step 8: Substitute SP = 5D: (5D - CP) / CP = 1/6. Step 9: Cross multiply: 6(5D - CP) = CP. Step 10: Expand: 30D - 6CP = CP. Step 11: Rearrange: 30D = 7CP → CP = (30/7)D. Step 12: Therefore, D : CP = D : (30/7 * D) = 7 : 30. Verification / Alternative check: Take a convenient discount value, for example D = Rs. 7. Then SP = 5D = Rs. 35 and M = 6D = Rs. 42. Discount percentage = (7 / 42) * 100 = 1/6 * 100 ≈ 16.67%. From CP = (30/7) * 7 = Rs. 30, profit = SP - CP = 35 - 30 = Rs. 5. Profit percent = (5 / 30) * 100 = 1/6 * 100 ≈ 16.67%. Thus both discount and profit percentages match, confirming that D : CP = 7 : 30 is correct. Why Other Options Are Wrong: Ratios such as 6:31, 11:30, 31:6 or 5:24 do not satisfy the simultaneous conditions SP = 5D and equal discount and profit percentages. Substituting any of these ratios into the equations would break either the relationship between SP and D or the equality of discount percent and profit percent. Common Pitfalls: A common mistake is to confuse discount percentage with discount amount or to treat SP as multiple of the percentage rather than of the amount. Another error is to set profit percentage equal to discount amount fraction without converting both to proper fractional forms. Writing all relationships algebraically and keeping track of which quantity is which prevents these errors. Final Answer: The required ratio of discount to cost price is 7:30.

Question 3

A man saves 20% of his monthly salary. Due to an increase in the cost of living, he has to increase his monthly expenses by 15%, and now he is able to save only Rs. 400 per month. What is his monthly salary?

Accepted Answer

Introduction / Context: This question combines percentage savings and percentage increase in expenses to determine the original salary. Initially the man saves a fixed proportion of his salary, and then due to a 15% rise in expenses his monthly saving drops to a fixed rupee amount. Such problems appear frequently in aptitude tests to check understanding of how savings, expenses and income relate to each other when percentages change. Given Data / Assumptions: Initially, the man saves 20% of his salary. Therefore, he spends 80% of his salary originally. His expenses then increase by 15%. After the increase, his remaining saving becomes Rs. 400 per month. His monthly salary remains the same before and after the increase. We must find the amount of his monthly salary. Concept / Approach: Let the salary be S. Initially, expenses = 0.80S and savings = 0.20S. When expenses increase by 15%, the new expenses become 1.15 times the old expenses, that is 1.15 * 0.80S. The new saving is then S minus these increased expenses. This new saving is given as Rs. 400. By equating S - 1.15 * 0.80S to 400, we get a simple linear equation in S which can be solved to obtain the salary. Step-by-Step Solution: Step 1: Let monthly salary = S rupees. Step 2: Initial saving = 20% of S = 0.20S. Step 3: Initial expenses = 80% of S = 0.80S. Step 4: Expenses increase by 15%, so new expenses = 0.80S * 1.15. Step 5: Compute new expenses factor: 0.80 * 1.15 = 0.92, so new expenses = 0.92S. Step 6: New saving = S - new expenses = S - 0.92S = 0.08S. Step 7: This new saving is given as Rs. 400, so 0.08S = 400. Step 8: Solve for S: S = 400 / 0.08 = 400 * (100 / 8) = 400 * 12.5 = Rs. 5,000. Verification / Alternative check: If S = Rs. 5,000, then initially he saves 20% of 5,000 = Rs. 1,000 and spends Rs. 4,000. After the rise, his new expenses are 4,000 * 1.15 = Rs. 4,600. His new saving is 5,000 - 4,600 = Rs. 400, which matches the information given in the question, confirming that the monthly salary is Rs. 5,000. Why Other Options Are Wrong: If the salary were Rs. 4,500, Rs. 6,000, Rs. 6,500, or Rs. 4,000, the new savings computed via the same percentage increases would not equal Rs. 400. For example, with S = 6,000, new expenses would be 0.92 * 6,000 = 5,520 and the new saving would be 6,000 - 5,520 = 480, which does not match the given saving. Common Pitfalls: A frequent error is to increase the salary instead of the expenses, or to misapply the 15% increase directly to the salary instead of to the original expenses. Another common mistake is to add 15 percentage points to the 80% expenses incorrectly, rather than multiplying by 1.15. Keeping track that expenses are a fraction of salary and that the increase applies to that fraction avoids these mistakes. Final Answer: The man's monthly salary is Rs. 5,000.

Question 4

A man purchases two articles. He sells one at a loss of 20% and the other at a profit of 25%, and overall he gains 5% on the whole transaction. What is the ratio of their selling prices (first article to second article)?

Accepted Answer

Introduction / Context: This is a slightly advanced profit and loss problem involving two articles sold with different loss and profit percentages but yielding an overall gain. The question specifically asks for the ratio of their selling prices rather than cost prices. To solve it, we must express the selling prices in terms of their cost prices and then use the condition on overall profit to derive an equation that links the cost prices. From this, the ratio of selling prices can be computed. Given Data / Assumptions: First article is sold at a loss of 20%. Second article is sold at a profit of 25%. Overall profit on the two articles together is 5%. Cost prices of the two articles may differ. We need the ratio of selling prices: SP1 : SP2. Concept / Approach: Let the cost prices of the two articles be C1 and C2. Then the corresponding selling prices are SP1 = 0.80C1 (20% loss) and SP2 = 1.25C2 (25% profit). The overall profit of 5% means that total selling price equals 1.05 times total cost price, i.e., SP1 + SP2 = 1.05(C1 + C2). Substituting the expressions for SP1 and SP2 gives a linear relationship between C1 and C2. Once we obtain the ratio C2 : C1, we can then compute SP1 : SP2 in terms of this ratio. Step-by-Step Solution: Step 1: Let cost prices be C1 and C2. Step 2: SP1 with 20% loss = 0.80C1. Step 3: SP2 with 25% profit = 1.25C2. Step 4: Overall profit of 5% gives: SP1 + SP2 = 1.05(C1 + C2). Step 5: Substitute SP1 and SP2: 0.80C1 + 1.25C2 = 1.05C1 + 1.05C2. Step 6: Rearrange: 0.80C1 - 1.05C1 + 1.25C2 - 1.05C2 = 0. Step 7: This simplifies to -0.25C1 + 0.20C2 = 0. Step 8: Hence 0.20C2 = 0.25C1, so C2 / C1 = 0.25 / 0.20 = 1.25 = 5/4. Step 9: Take C1 = 4k and C2 = 5k for some k. Step 10: SP1 = 0.80C1 = 0.80 * 4k = 3.2k. Step 11: SP2 = 1.25C2 = 1.25 * 5k = 6.25k. Step 12: Therefore, SP1 : SP2 = 3.2k : 6.25k = 3.2 : 6.25. Step 13: Multiply both terms by 100 to clear decimals: 3.2 : 6.25 = 320 : 625. Step 14: Simplify if possible; 320 and 625 have no common factor other than 5, so divide both by 5: 320/5 = 64, 625/5 = 125, giving 64 : 125. Verification / Alternative check: Using C1 = 4k and C2 = 5k with k = 1 for simplicity, total CP = 4 + 5 = 9 units. SP1 = 3.2 units and SP2 = 6.25 units, total SP = 9.45 units. Profit = 9.45 - 9 = 0.45, so profit percent = (0.45 / 9) * 100 = 5%. Thus, the found ratio of selling prices 64 : 125 is fully consistent with the overall 5% profit condition. Why Other Options Are Wrong: Ratios such as 4 : 5, 5 : 4, 16 : 25 or 25 : 16 do not satisfy the required balance between individual profit and loss percentages and the overall 5% gain when you compute the corresponding cost price ratios. Only 64 : 125 leads to a combined selling price that is exactly 105% of the total cost price. Common Pitfalls: A common mistake is to assume that the cost prices are equal and then attempt to average the profit and loss percentages, which will not give the correct overall 5% gain. Another error is to try and deduce the ratio of selling prices directly from the profit and loss percentages without forming the overall equation SP1 + SP2 = 1.05(C1 + C2). Proper algebraic setup is essential here. Final Answer: The ratio of their selling prices is 64 : 125 (first article to second article).

Question 5

Selling an article at a profit of 20%, Aman receives Rs. 400 more than if he sells it at a loss of 20%. What is the cost price of the article?

Accepted Answer

Introduction / Context: This question compares two different selling scenarios of the same article: one with a 20% profit and the other with a 20% loss. The difference between the two selling prices is given in rupees. This is a classic type of problem where we can exploit the symmetry in percentages above and below cost price to derive the cost price using a simple linear equation. Given Data / Assumptions: Profit scenario: article is sold at 20% profit. Loss scenario: article is sold at 20% loss. Difference in selling prices between the two scenarios = Rs. 400. The underlying cost price is the same in both scenarios. We must find the cost price (CP) of the article. Concept / Approach: Let CP be C. When sold at 20% profit, the selling price is 1.20C. When sold at 20% loss, the selling price is 0.80C. The difference between these two selling prices is given as Rs. 400. Therefore, 1.20C - 0.80C = 0.40C must equal 400. Solving this simple equation gives us the cost price. Because the percentages are symmetrically placed around the cost price, the difference comes out as a neat fraction of CP. Step-by-Step Solution: Step 1: Let cost price be C rupees. Step 2: Selling price at 20% profit, SP1 = C * (1 + 20/100) = 1.20C. Step 3: Selling price at 20% loss, SP2 = C * (1 - 20/100) = 0.80C. Step 4: Given that SP1 - SP2 = Rs. 400. Step 5: Substitute SP1 and SP2: 1.20C - 0.80C = 400. Step 6: Simplify left side: (1.20 - 0.80)C = 0.40C. Step 7: So 0.40C = 400. Step 8: Therefore, C = 400 / 0.40 = 400 * (10 / 4) = 400 * 2.5 = 1,000. Verification / Alternative check: If CP = Rs. 1,000, then SP1 at 20% profit = 1.20 * 1,000 = Rs. 1,200. SP2 at 20% loss = 0.80 * 1,000 = Rs. 800. Difference between the two selling prices = 1,200 - 800 = Rs. 400, which matches the given information exactly and confirms the cost price. Why Other Options Are Wrong: If CP were Rs. 900, for example, the difference in selling prices would be 0.40 * 900 = Rs. 360, not 400. Similarly, cost prices of Rs. 1,020, Rs. 1,140 or Rs. 1,210 would lead to differences of 0.40C that are not equal to Rs. 400. Only Rs. 1,000 makes 0.40C exactly equal to 400. Common Pitfalls: Some learners wrongly take 20% of Rs. 400 or try to treat 400 as a percentage directly. Others confuse the base for percentages and do not realise that both 20% profit and 20% loss are taken on the same cost price. Writing out both selling prices in terms of cost price and then subtracting them is the cleanest and most reliable method. Final Answer: The cost price of the article is Rs. 1000.

Question 6

A shopkeeper expects a gain of (45/2)% on his cost price. If his actual sale value is Rs. 392, what is the amount of profit he makes?

Accepted Answer

Introduction / Context: This problem involves a fractional percentage gain on the cost price and a known selling price. The percentage gain is given as 45/2 percent, which equals 22.5%. The selling price is known, and we are asked to find the absolute profit. To do this, we must first compute the cost price using the relationship between cost price, profit percentage and selling price, and then subtract the cost price from the selling price. Given Data / Assumptions: Expected gain = (45/2)% = 22.5% on cost price. Selling price (SP) = Rs. 392. Gain percentage is based on cost price. We assume the shopkeeper actually achieves this expected gain. We must find the profit in rupees. Concept / Approach: If profit is p% on cost price, then selling price equals cost price multiplied by (1 + p/100). Here, p = 22.5. Let cost price be C. Then SP = C * (1 + 22.5/100) = 1.225C. Since SP is given, we can write 392 = 1.225C and solve for C. Finally, profit is SP - C. Working with the decimal 1.225 is straightforward if we treat it as the fraction 49/40 or 1225/1000 depending on convenience. Step-by-Step Solution: Step 1: Gain percentage = 45/2% = 22.5%. Step 2: Let cost price be C rupees. Step 3: Selling price SP = C * (1 + 22.5/100) = C * 1.225. Step 4: Given SP = 392, so 1.225C = 392. Step 5: Express 1.225 as a fraction: 1.225 = 1225/1000 = 49/40. Step 6: Thus, (49/40) * C = 392. Step 7: Multiply both sides by 40: 49C = 392 * 40. Step 8: Compute 392 * 40 = 15,680. Step 9: So C = 15,680 / 49 = 320. Step 10: Profit = SP - CP = 392 - 320 = 72. Verification / Alternative check: With CP = Rs. 320 and gain percentage = 22.5%, profit should be 22.5% of 320. Compute 10% of 320 = 32, 20% = 64, 2.5% = 8, so 22.5% = 64 + 8 = 72. Selling price = 320 + 72 = 392, which matches the given SP. This confirms that the profit of Rs. 72 is correct. Why Other Options Are Wrong: Profits of Rs. 70, Rs. 74, Rs. 76 or Rs. 68 would not correspond to a gain of exactly 22.5% on the implied cost price. When recomputed, they would give slightly different selling prices or slightly different percentages. Only a profit of Rs. 72 maintains the exact 22.5% gain with an SP of Rs. 392. Common Pitfalls: Many learners misread 45/2% as 45.2% or incorrectly convert it to a decimal. Others treat 22.5% as if it is applied to the selling price rather than the cost price. Converting the percentage to a clear fraction and writing SP = (1 + p/100) * CP are reliable ways to avoid confusion. Final Answer: The shopkeeper's profit is Rs. 72.

Question 7

Manisha goes to a shop with a certain amount of money. With this amount she can buy either 50 Chocobars or 40 Fivestar chocolates. She spends 10% of the amount on petrol and, out of the remaining balance, buys 20 Fivestar chocolates and some Chocoba…

Accepted Answer

Introduction / Context: This question combines ratio, unitary method and percentage spending. Manisha can use a fixed amount either to buy a certain number of Chocobars or a certain number of Fivestar chocolates, which implies a relationship between their individual prices. After spending part of the money on petrol, she buys a combination of the two types of chocolates. The task is to determine how many Chocobars she can purchase with the remaining amount. Given Data / Assumptions: With her total amount A, she can buy 50 Chocobars. With the same amount A, she can buy 40 Fivestar chocolates. She spends 10% of A on petrol. From the remaining 90% of A, she buys 20 Fivestar chocolates and some Chocobars. We need to find the number of Chocobars she buys from the remaining money. Concept / Approach: Let the price of one Chocobar be C and the price of one Fivestar be F. From the initial information, total amount A equals 50C and also equals 40F. This allows us to express F in terms of C. After spending 10% on petrol, the remaining amount is 0.9A. We compute the cost of 20 Fivestars and subtract this from 0.9A to see how much money remains for Chocobars. Dividing that remainder by the price per Chocobar gives the required number of Chocobars. Step-by-Step Solution: Step 1: Let total amount be A rupees. Step 2: Let price of one Chocobar = C and price of one Fivestar = F. Step 3: From A = 50C and A = 40F, we get 50C = 40F. Step 4: Therefore, F = (50/40)C = (5/4)C = 1.25C. Step 5: She spends 10% of A on petrol, so remaining money = 0.9A. Step 6: Since A = 50C, remaining money = 0.9 * 50C = 45C. Step 7: She buys 20 Fivestars, so cost of these = 20F = 20 * 1.25C = 25C. Step 8: Money left for Chocobars = 45C - 25C = 20C. Step 9: Number of Chocobars she can buy = (money left) / (price per Chocobar) = 20C / C = 20. Verification / Alternative check: Assume specific prices for clarity: take C = Rs. 2. Then A = 50 * 2 = Rs. 100 and F = 1.25 * 2 = Rs. 2.50. After spending 10% of 100 on petrol, she has Rs. 90. Cost of 20 Fivestars = 20 * 2.50 = Rs. 50. Remaining amount = 90 - 50 = Rs. 40. Each Chocobar costs Rs. 2, so she can buy 40 / 2 = 20 Chocobars, which confirms the result. Why Other Options Are Wrong: If she could buy 24, 26, 28 or 22 Chocobars, the total money spent on chocolates plus petrol would no longer equal her original amount A when we use the derived price relationship F = 1.25C. A full recomputation with those quantities shows mismatched totals, making them inconsistent with the given conditions. Common Pitfalls: Students sometimes overlook that the same initial amount is used for both purchasing scenarios, leading to an incorrect relationship between C and F. Another common error is to apply the 10% deduction incorrectly, for example subtracting from the number of chocolates instead of the money. Carefully translating each step into algebra with the correct base amounts avoids such mistakes. Final Answer: Manisha can buy 20 Chocobars with the remaining money.

Question 8

Mahesh buys 100 kg of rice for Rs. 1,040. He then sells the rice at such a rate that his loss in rupees is equal to the money he receives for 30 kg of rice. At what price per kilogram does he sell the rice?

Accepted Answer

Introduction / Context: This question involves cost price per kilogram, selling price per kilogram and a condition that ties the total loss to the revenue from a specific quantity. Mahesh buys rice in bulk and sells it at a uniform rate per kilogram. The interesting twist is that his total loss equals the amount he earns from selling 30 kg of rice. This allows us to set up an equation relating total loss and selling price and solve for the selling price per kilogram. Given Data / Assumptions: Total quantity of rice bought = 100 kg. Total cost price = Rs. 1,040. Therefore, cost price per kg is constant. He sells all rice at a single uniform selling price per kg, say x rupees. His total loss in rupees equals the money he receives for 30 kg of rice. We need to find the selling price per kg, x. Concept / Approach: First, we compute the cost price per kg by dividing total cost by total kilograms purchased. Let selling price per kg be x. Then total selling price for 100 kg is 100x. Loss equals total cost price minus total selling price. The condition states that this loss equals the revenue from 30 kg of rice, which is 30x. Therefore, we set total loss = 30x and solve the resulting equation for x. Step-by-Step Solution: Step 1: Total cost price = Rs. 1,040 for 100 kg. Step 2: Cost price per kg = 1,040 / 100 = Rs. 10.40. Step 3: Let selling price per kg = x rupees. Step 4: Total selling price for 100 kg = 100x rupees. Step 5: Total loss = total cost price - total selling price = 1,040 - 100x. Step 6: Given that loss equals the money received for 30 kg, so 1,040 - 100x = 30x. Step 7: Rearrange: 1,040 = 100x + 30x = 130x. Step 8: Therefore, x = 1,040 / 130. Step 9: Compute x: 1,040 / 130 = 8, so selling price per kg = Rs. 8. Verification / Alternative check: At Rs. 8 per kg, total selling price for 100 kg = 100 * 8 = Rs. 800. Total cost price = Rs. 1,040, so loss = 1,040 - 800 = Rs. 240. Money received for 30 kg at Rs. 8 per kg is 30 * 8 = Rs. 240. Thus, total loss equals the revenue from 30 kg, precisely matching the given condition. Why Other Options Are Wrong: If the selling price per kg were Rs. 7.46, Rs. 8.74, Rs. 8.56 or Rs. 7.80, the revenue from 30 kg would not equal the total loss when calculated with the same total cost of Rs. 1,040. For example, at Rs. 7.80, total SP for 100 kg is Rs. 780, loss is Rs. 260, but revenue on 30 kg is only Rs. 234, which does not match the loss. Common Pitfalls: A typical mistake is to equate the loss per kg to the price of 30 kg or to forget that the loss is computed on the entire 100 kg. Another error is to misinterpret the condition and set 100x - 1,040 = 30x instead of 1,040 - 100x = 30x. Carefully identifying that loss equals cost price minus selling price and that the loss is on the whole stock avoids these issues. Final Answer: Mahesh sells the rice at Rs. 8/kg.

Question 9

A retailer buys goods from a shopkeeper at a discount of 40% on the list (marked) price and sells them to customers at a discount of 25% on the same list price. What is the retailer's profit percentage?

Accepted Answer

Introduction / Context: This question deals with successive discounts on the same marked price, one from the wholesaler to the retailer and another from the retailer to the final customer. The retailer purchases goods below the marked price and sells them at a higher price, but still below the marked price. The task is to compute the profit percentage made by the retailer relative to his cost price. This is a standard application of percentages in trade and commerce. Given Data / Assumptions: Marked price (list price) of the goods = M (assume M rupees). Retailer buys goods at 40% discount from M. Retailer sells the goods at 25% discount from M to customers. We ignore transport or other overhead costs; only purchase and sale discounts matter. We must find profit percentage on the retailer's cost price. Concept / Approach: The retailer's cost price is the price at which he buys the goods from the shopkeeper. A 40% discount on M means he pays 60% of M, or 0.60M. The retailer's selling price to customers is 75% of M, or 0.75M, since he offers a 25% discount on the marked price. Profit percentage is computed as (SP - CP) / CP * 100, where CP is the retailer's purchase price and SP is the retailer's selling price. Step-by-Step Solution: Step 1: Let marked price be M rupees. Step 2: Retailer buys at 40% discount, so his cost price CP = M * (1 - 40/100) = 0.60M. Step 3: Retailer sells at 25% discount, so his selling price SP = M * (1 - 25/100) = 0.75M. Step 4: Profit made by retailer = SP - CP = 0.75M - 0.60M = 0.15M. Step 5: Profit percentage on CP = (Profit / CP) * 100 = (0.15M / 0.60M) * 100. Step 6: Simplify fraction: 0.15M / 0.60M = 0.25 = 1/4. Step 7: Profit percentage = 0.25 * 100 = 25%. Verification / Alternative check: Assume a simple marked price, for example M = Rs. 100. Retailer's cost price at 40% discount = Rs. 60. Retailer's selling price at 25% discount = Rs. 75. Profit = 75 - 60 = Rs. 15. Profit percentage on CP = (15 / 60) * 100 = 25%. This numerical example confirms the symbolic calculation with M and shows clearly how the profit arises in practice. Why Other Options Are Wrong: Profit percentages of 10%, 15% or 20% would require different relative positions of CP and SP than the ones arising from 40% and 25% discounts on the same marked price. A profit of 5% is far too small for the difference between Rs. 60 and Rs. 75. Only 25% matches the actual comparison between CP and SP. Common Pitfalls: Some learners mistakenly subtract the discount percentages (40% - 25% = 15%) and assume 15% is the profit. Others confuse discount on marked price with profit on cost price, which are based on different denominators. Always convert each discount to an actual price, then compute profit relative to the cost price to obtain the correct profit percentage. Final Answer: The retailer earns a profit of 25% on his cost price.

Question 10

Sreya buys a plot for Rs. 6,00,000. She sells half of the plot at a profit of 10% and the remaining half at a profit of 15%. What is her overall profit percentage on the entire investment?

Accepted Answer

Introduction / Context: Real estate profit problems often involve selling different portions of an asset at different profit rates. In this question, Sreya buys a plot, sells half of it at one profit percentage and the other half at a higher profit percentage. We must find the overall profit percentage on her entire investment. This requires computing the total selling price from both parts and comparing it with the total cost price. Given Data / Assumptions: Total cost price of the plot = Rs. 6,00,000. Half of the plot is sold at 10% profit. The remaining half is sold at 15% profit. The halves are equal in cost because the plot is assumed uniform. We must find net profit percentage on the full Rs. 6,00,000. Concept / Approach: First, we split the total cost price into two equal parts, each corresponding to half of the plot. For each half, we compute the selling price by applying the given profit percentage: 10% on the first half and 15% on the second half. Adding these two selling prices gives the total selling price. The overall profit is total SP minus total CP. Finally, we divide the profit by the total CP and multiply by 100 to get the overall profit percentage. This is an example of a weighted average of profit percentages, but since both halves have equal cost, the computation is straightforward. Step-by-Step Solution: Step 1: Total cost price, CP_total = Rs. 6,00,000. Step 2: Cost of each half = 6,00,000 / 2 = Rs. 3,00,000. Step 3: First half is sold at 10% profit, so SP1 = 3,00,000 * 1.10 = Rs. 3,30,000. Step 4: Second half is sold at 15% profit, so SP2 = 3,00,000 * 1.15 = Rs. 3,45,000. Step 5: Total selling price, SP_total = SP1 + SP2 = 3,30,000 + 3,45,000 = Rs. 6,75,000. Step 6: Overall profit = SP_total - CP_total = 6,75,000 - 6,00,000 = Rs. 75,000. Step 7: Overall profit percentage = (75,000 / 6,00,000) * 100. Step 8: Simplify: 75,000 / 6,00,000 = 75 / 600 = 1 / 8, so profit percentage = (1/8) * 100 = 12.5%. Verification / Alternative check: Since both equal halves have the same cost, the overall profit percentage can also be seen as the simple average of 10% and 15%, which is (10 + 15) / 2 = 12.5%. This matches the detailed calculation. This shortcut works because the cost bases of both halves are identical; if they were different, we would need a weighted average based on cost values. Why Other Options Are Wrong: Values such as 13.8%, 11.4%, 14.5% or 10.5% do not equal the exact fraction 1/8 of the total cost price. Recomputing with those percentages would give total selling prices that differ from 6,75,000. Only 12.5% corresponds to an increase of Rs. 75,000 on Rs. 6,00,000. Common Pitfalls: A common mistake is to average the profit percentages even when the cost bases are not equal in other problems, leading to incorrect results. Here they happen to be equal, but learners should remember to check the cost distribution before averaging. Another error is to miscalculate 10% and 15% profits on Rs. 3,00,000 or to forget to sum the selling prices correctly. Final Answer: Sreya's overall profit percentage on the plot is 12.5 %.

Question 11

A salesman calculates his profit on the marked (list) price and finds it to be 30%. He forgets that he actually gave a discount of 20% to the customer. What is his actual profit percentage on the cost price?

Accepted Answer

Introduction / Context: This question explores the difference between profit calculated on marked price and the actual profit when a discount is given. The salesman incorrectly computes his profit as 30% of the marked price, ignoring the 20% discount he has granted. We must determine the true profit percentage on the cost price. This involves understanding the relationships between marked price, cost price, discount and actual selling price. Given Data / Assumptions: Let marked price be M rupees. The salesman thinks his profit is 30% of the marked price. Thus, he assumes (M - cost price) / M = 30%. He actually gives a discount of 20%, so the real selling price is 80% of M. We need the actual profit percentage based on cost price. Concept / Approach: The salesman says his profit on the marked price is 30%, which we interpret as (M - CP) / M = 0.30, where CP is cost price. From this we can find CP in terms of M. The real selling price must be SP = 0.80M, because of the 20% discount. Then actual profit on cost price is (SP - CP) / CP * 100. The key step is to correctly understand that his 30% is calculated on M, not on CP, and that he forgets the discount when making this calculation. Step-by-Step Solution: Step 1: Let marked price = M and cost price = CP. Step 2: Salesman calculates profit on M, so (M - CP) / M = 30/100 = 0.30. Step 3: Therefore, M - CP = 0.30M. Step 4: Rearranging: CP = M - 0.30M = 0.70M. Step 5: He actually gives 20% discount, so true selling price SP = 0.80M. Step 6: Actual profit = SP - CP = 0.80M - 0.70M = 0.10M. Step 7: Actual profit percentage on CP = (0.10M / 0.70M) * 100. Step 8: Simplify fraction: 0.10M / 0.70M = (1/10) / (7/10) = 1/7. Step 9: Profit percentage = (1/7) * 100 = 100/7% ≈ 14.2857%. Verification / Alternative check: Choose a convenient marked price, say M = Rs. 700. From CP = 0.70M, we get CP = Rs. 490. According to his mistaken calculation, he thinks profit is M - CP = 700 - 490 = Rs. 210, which is 30% of 700. In reality, he sells at a 20% discount: SP = 0.80 * 700 = Rs. 560. Actual profit is 560 - 490 = Rs. 70. Profit percentage on CP = (70 / 490) * 100 = (1/7) * 100 = 100/7%, confirming our result. Why Other Options Are Wrong: A profit of 60% would require SP = 1.6CP, far above 0.80M, while 22.5%, 18.4% or 260/11% (which is about 23.64%) do not match the exact fraction 1/7 arising from the proper equations. Only 100/7% aligns with both the given mistaken calculation and the actual discount applied. Common Pitfalls: Many candidates misinterpret the phrase "profit on the marked price" and accidentally compute (SP - CP) / CP = 30% or equate profit directly to 30% of cost price. Others forget to apply the discount to the marked price when determining the actual selling price. Carefully distinguishing which base the percentage refers to, and systematically expressing all values in terms of M, prevents these mistakes. Final Answer: The salesman's actual profit percentage is 100/7%, which is approximately 14.29%.

Question 12

If the cost price of a certain article doubles, then the loss in rupees becomes three times what it was initially (selling price remains the same). What was the initial loss percentage on the cost price?

Accepted Answer

Introduction / Context: This question examines the effect of changing cost price while keeping the selling price constant. The loss in rupees is said to become three times its original value when the cost price doubles. We must find what the original loss percentage was. This type of question checks conceptual understanding of how profit and loss amounts relate to cost price and selling price through basic algebraic relationships. Given Data / Assumptions: Original cost price = C (unknown). Original selling price = S (unchanged later). Original loss = C - S (assuming C > S). New cost price after doubling = 2C. New loss = 2C - S. Given that new loss = 3 × original loss. We must find original loss percentage = (C - S) / C * 100. Concept / Approach: We set up an equation that the new loss equals three times the original loss: 2C - S = 3(C - S). This involves only C and S. Solving this equation gives a relationship between S and C. Once we know S in terms of C, we can substitute into the expression for loss percentage (C - S) / C * 100. Since C cancels in the ratio, we obtain a numeric percentage without needing actual values for C or S. Step-by-Step Solution: Step 1: Original loss = C - S. Step 2: New cost price = 2C, selling price is still S, so new loss = 2C - S. Step 3: Given that new loss is three times original loss: 2C - S = 3(C - S). Step 4: Expand right side: 3(C - S) = 3C - 3S. Step 5: Equation becomes 2C - S = 3C - 3S. Step 6: Rearrange: 2C - S - 3C + 3S = 0 → -C + 2S = 0. Step 7: So 2S = C, hence S = C/2. Step 8: Original loss = C - S = C - C/2 = C/2. Step 9: Loss percentage = (original loss / cost price) * 100 = (C/2) / C * 100 = (1/2) * 100 = 50%. Verification / Alternative check: Choose C = Rs. 100 for simplicity. Then S = C/2 = Rs. 50. Original loss = 100 - 50 = Rs. 50. New cost price = 200, selling price still 50, new loss = 200 - 50 = Rs. 150. Compare: new loss is 150, original loss was 50, and 150 = 3 × 50. Original loss percent = (50 / 100) * 100 = 50%, which matches our algebraic result. Why Other Options Are Wrong: Loss percentages of 25%, 75%, 40% or 0% do not give the exact threefold relationship when cost price is doubled and selling price is held constant. For example, with 25% loss, the algebraic relationship 2C - S = 3(C - S) would not hold. Only 50% loss creates the exact multiplication of the loss amount as described in the question. Common Pitfalls: A common error is to try to guess percentages without setting up the equation, or to incorrectly assume that doubling cost price doubles the loss percentage. Another mistake is mixing up the roles of cost and selling price when writing the loss expressions. Writing everything in terms of C and S and proceeding step by step avoids such confusion. Final Answer: The initial loss percentage on the article was 50 %.

Question 13

Arun purchases 30 kg of wheat at Rs. 11.50 per kg and 20 kg of wheat at Rs. 14.25 per kg. He mixes the two varieties and sells the mixture. At approximately what selling price per kg should he sell the mixture to make a profit of 30%?

Accepted Answer

Introduction / Context: This is a mixture and profit problem. Arun buys two different lots of wheat at different prices per kilogram, mixes them, and then sells the mixture at a uniform price. To find the selling price per kg that yields a desired profit percentage, we must first compute the average cost price per kg of the mixture and then apply the profit percentage to this average cost. Such questions are common in competitive exams and test the ability to handle weighted averages and percentage gain together. Given Data / Assumptions: First lot: 30 kg at Rs. 11.50 per kg. Second lot: 20 kg at Rs. 14.25 per kg. Total quantity after mixing = 30 + 20 = 50 kg. Required profit on the mixture = 30%. The mixture is sold at a single uniform rate per kg. Concept / Approach: We first compute the total cost price of both lots combined. Dividing the total cost by the total quantity gives the average cost price per kg of the mixture. To achieve a 30% profit, the selling price per kg must be 130% of this average cost price, i.e., 1.30 times the average cost. After computing this value, we compare it with the answer options and select the closest approximate value, as the question asks for an approximate price. Step-by-Step Solution: Step 1: Cost of first lot = 30 kg * Rs. 11.50/kg = Rs. 345. Step 2: Cost of second lot = 20 kg * Rs. 14.25/kg = Rs. 285. Step 3: Total cost = 345 + 285 = Rs. 630. Step 4: Total quantity = 30 + 20 = 50 kg. Step 5: Average cost price per kg of mixture = total cost / total quantity = 630 / 50 = Rs. 12.60. Step 6: Required selling price per kg to get 30% profit = 1.30 * 12.60. Step 7: Compute 1.30 * 12.60 = 12.60 + 0.30 * 12.60 = 12.60 + 3.78 = Rs. 16.38. Step 8: The nearest option to Rs. 16.38 is Rs. 16.30. Verification / Alternative check: If Arun sells the 50 kg mixture at Rs. 16.30 per kg, his total selling price will be approximately 16.30 * 50 = Rs. 815. Total cost is Rs. 630, so profit is about 815 - 630 = Rs. 185. Profit percentage ≈ (185 / 630) * 100 ≈ 29.37%, which is close to 30% and acceptable for an approximate answer. If he sold at Rs. 17.80, the profit percentage would be much higher than 30%, so 16.30 is the best fit among the options. Why Other Options Are Wrong: Selling at Rs. 14 or Rs. 15.40 per kg would yield profits far below 30% when compared to the average cost of Rs. 12.60. Selling at Rs. 17.80 or Rs. 15.80 would give profit percentages significantly above 30%. Among the given choices, only Rs. 16.30 per kg approximates the 30% profit requirement based on the computed value of Rs. 16.38. Common Pitfalls: Some learners incorrectly average the two buying prices directly without weighting by quantities, or they attempt to apply 30% profit separately on each lot instead of on the mixture. Another common mistake is to miscalculate the total cost or the average cost by forgetting to divide by total quantity. Always compute a weighted average using total cost divided by total quantity before applying the profit percentage. Final Answer: Arun should sell the mixture at approximately Rs. 16.30 per kg to earn about 30% profit.

Question 14

In a shop, the cost price of an article is 54% of its marked price. If the shopkeeper allows a discount of 15% on the marked price, what percentage profit does he earn on this article?

Accepted Answer

Introduction / Context: This profit and loss question combines the ideas of marked price, cost price, discount and percentage gain. Many competitive exams test whether you can move step by step from marked price to selling price and then compare with cost price. Understanding the chain MP → SP → CP is essential to avoid simple mistakes that lead to the wrong profit percentage. Given Data / Assumptions: Cost price (CP) is 54% of the marked price (MP). A discount of 15% is allowed on the marked price. We need to find the percentage profit on cost price. Assume the article is sold once and there are no other hidden costs or taxes. Concept / Approach: The standard approach is to treat the marked price as a convenient base, usually 100 units of money. From that, cost price and selling price are expressed as percentages of this base. Once we know both CP and SP numerically, the profit percentage is calculated using the formula: profit% = (SP - CP) / CP * 100. Using a simple assumed MP keeps the calculations clean and general. Step-by-Step Solution: Assume marked price MP = 100 units.Then cost price CP = 54% of 100 = 54 units.Discount = 15% of MP, so selling price SP = 100 - 15 = 85 units.Profit = SP - CP = 85 - 54 = 31 units.Profit percentage = (31 / 54) * 100 ≈ 57.4%. Verification / Alternative check: You could also choose MP = 1000 or any other convenient value. For example, if MP = 1000, then CP = 540 and SP = 850. Profit = 310, and profit% = (310 / 540) * 100, which again gives approximately 57.4%. Because ratios are preserved, any consistent base for MP leads to the same percentage result. Why Other Options Are Wrong: 51.32 %, 49.23 % and 46.8 % are all less than the correct value and typically arise from errors such as taking profit over marked price instead of cost price, or misapplying the discount on cost price instead of marked price. These small numerical slips change the denominator and give a smaller profit percentage than is actually earned. Common Pitfalls: A common mistake is to subtract 15 from 54 directly or to treat 54% and 15% on the same base without checking which is applied to the marked price and which is applied to cost price. Another frequent error is to compute profit% as profit divided by selling price instead of cost price. Always remember that percentage profit or loss is defined on cost price unless explicitly stated otherwise in the question. Final Answer: The shopkeeper earns a profit of approximately 57.4 % on the article.

Question 15

Raju sells an article at a discount of 8% for Rs 17,940 and still makes a profit of 19.6% on the cost price. If he sells the article without offering any discount, what profit percentage would he earn?

Accepted Answer

Introduction / Context: This problem checks your understanding of how discount, marked price, cost price and profit percentage are related. Raju sells an article with a discount and still earns profit. We must reverse engineer the cost price and then see what happens if the discount is removed. Such questions are very common in aptitude tests and require systematic use of percentage formulas. Given Data / Assumptions: Selling price with discount (SP₁) = Rs 17,940. Discount allowed = 8% on marked price. Profit at this selling price = 19.6% on cost price. If no discount is given, selling price becomes equal to the marked price (MP). We need the new profit percentage without discount. Concept / Approach: First, use the profit information at SP₁ to find the cost price. Then, use the discount relation to find the marked price. When the discount is removed, the new selling price equals MP. Finally, compute the profit percentage using the formula profit% = (SP - CP) / CP * 100. Doing the steps in this order prevents mixing up MP, CP and SP. Step-by-Step Solution: Step 1: Let cost price = CP. Given profit at SP₁ is 19.6%, so SP₁ = 1.196 * CP.Step 2: 17,940 = 1.196 * CP ⇒ CP = 17,940 / 1.196 = 15,000.Step 3: 8% discount means SP₁ = 92% of MP. So 17,940 = 0.92 * MP ⇒ MP = 17,940 / 0.92 = 19,500.Step 4: Without discount, new SP = MP = Rs 19,500.Step 5: Profit in this case = 19,500 - 15,000 = 4,500, so profit% = (4,500 / 15,000) * 100 = 30%. Verification / Alternative check: You can double check by recomputing with the obtained values. At CP = 15,000 and SP₁ = 17,940, profit = 2,940 which is indeed 19.6% of 15,000. At SP = 19,500, the profit of 4,500 over 15,000 clearly gives 30%. This confirms that no arithmetic error has occurred in the percentage calculations. Why Other Options Are Wrong: 27%, 32% and 25% come from typical mistakes such as using the discount percent on cost price instead of marked price, or mixing up 1.196 and 0.196 while forming equations. They do not satisfy both conditions of the problem simultaneously. Only 30% fits the conditions of both the given discount case and the no-discount case. Common Pitfalls: Students often try to jump directly from the discounted selling price to the new profit percentage without first finding the cost price and marked price separately. Another mistake is to treat the 8% discount as applied to cost price, which is incorrect. Always remember that discount is calculated on the marked price and profit or loss is calculated on the cost price unless specifically stated otherwise. Final Answer: If Raju sells without any discount, his profit percentage becomes 30%.

Question 16

Uma sells an article for Rs 3,400 and earns a profit of 25% on its cost price. If instead she had sold the article for Rs 3,265, what profit percentage would she have obtained?

Accepted Answer

Introduction / Context: This profit and loss question is about changing the selling price while the cost price remains the same. When the selling price changes, the profit percentage also changes. The key idea is to first compute the cost price from one known selling price and profit percentage, and then use that cost price to compute a new profit percentage with a different selling price. Given Data / Assumptions: First selling price (SP₁) = Rs 3,400. Profit at SP₁ = 25% of cost price. Second selling price (SP₂) = Rs 3,265. Cost price (CP) of the article remains the same in both cases. We need to find the profit percentage at SP₂. Concept / Approach: The formula connecting cost price and selling price with profit percentage is SP = CP * (1 + profit%). When the profit percentage is given, we can find CP from SP. Afterwards we use the same CP with the new SP to compute profit% again using profit% = (SP - CP) / CP * 100. Understanding that CP does not change is crucial for solving such problems correctly. Step-by-Step Solution: Step 1: Let cost price be CP. Given that SP₁ = 3,400 with 25% profit, so 3,400 = CP * 1.25.Step 2: CP = 3,400 / 1.25 = 2,720.Step 3: With SP₂ = 3,265, profit₂ = SP₂ - CP = 3,265 - 2,720 = 545.Step 4: Profit percentage at SP₂ = (545 / 2,720) * 100 ≈ 20.04%.Step 5: This is approximately equal to 20%, matching one of the options. Verification / Alternative check: Using CP = 2,720, a 20% profit would mean SP = 2,720 * 1.20 = 3,264. The given SP₂ is 3,265, only Re 1 higher, which is within rounding and option approximation. So 20% is the best and correct choice. None of the other options align closely with the computed profit percentage. Why Other Options Are Wrong: 22%, 27% and 18% differ significantly from the calculated profit of roughly 20%. To reach 22% or 27%, the selling price would need to be much higher. For 18%, the selling price would need to be lower. As these do not fit the actual numbers given, they are incorrect distractors. Common Pitfalls: A common mistake is to apply 25% directly on 3,400 or to try to find the second profit without first computing the true cost price. Another error is to treat the difference between 3,400 and 3,265 as directly related to profit percentage without referencing CP. Always anchor all percentage profit calculations to the cost price, not just the selling price differences. Final Answer: If Uma had sold the article for Rs 3,265, her profit percentage would have been approximately 20%.

Question 17

Namitha sells a power bank for Rs 1,950 at a loss of 25% on its cost price. At what price should she sell the same power bank to earn a profit of 25% on the cost price?

Accepted Answer

Introduction / Context: This is a classic cost price and selling price conversion question where the article is first sold at a loss and later is to be sold at a profit. You are given one selling price and the loss percentage, and you must then calculate another selling price for a desired profit percentage. Such questions test your ability to move between different percentage conditions using the same cost price. Given Data / Assumptions: Current selling price SP₁ = Rs 1,950. Loss at SP₁ = 25% of cost price. The same power bank should now be sold at a profit of 25% on the cost price. We assume cost price of the article does not change. We need to find the new selling price SP₂. Concept / Approach: If an item is sold at a loss of L%, then SP = (1 - L%) * CP. Similarly, for a profit of P%, SP = (1 + P%) * CP. So we first find the cost price from the loss case, and then use it to compute the selling price for the desired profit. This two-step method is straightforward and avoids confusion between loss and profit conditions. Step-by-Step Solution: Step 1: Let cost price = CP.Step 2: A loss of 25% implies SP₁ = 0.75 * CP.Step 3: Given SP₁ = 1,950, so 1,950 = 0.75 * CP ⇒ CP = 1,950 / 0.75 = 2,600.Step 4: To gain 25%, new SP₂ must be 1.25 * CP = 1.25 * 2,600 = 3,250.Step 5: Therefore, the required selling price is Rs 3,250. Verification / Alternative check: Check the calculations from cost price. Selling at 1,950 means loss = 2,600 - 1,950 = 650, and loss% = (650 / 2,600) * 100 = 25%, which matches the given data. Selling at 3,250 gives profit = 3,250 - 2,600 = 650, and profit% = (650 / 2,600) * 100 = 25%. Both conditions are satisfied, confirming that our cost price and new selling price are correct. Why Other Options Are Wrong: Values like Rs 3,680, Rs 3,560 and Rs 3,320 correspond to much higher or lower profit percentages when compared to the cost price of Rs 2,600. They do not give exactly 25% profit, so they cannot be correct. They are included as plausible looking numbers to test whether you have applied the formulas correctly. Common Pitfalls: Learners sometimes assume that the difference between the loss selling price and the profit selling price must be a fixed amount like Rs 1,300 or try to apply percentages directly on the selling prices rather than cost price. Always remember that both loss% and profit% are calculated on cost price. Mixing bases leads to wrong answers in percentage questions. Final Answer: Namitha must sell the power bank for Rs. 3250 to earn a 25% profit on the cost price.

Question 18

A dishonest seller gives only 840 grams of goods to customers while charging them for 1 kilogram. He also claims that he is selling at a loss of 4% on cost price. What is his actual percentage profit or loss?

Accepted Answer

Introduction / Context: This question combines two core ideas from profit and loss: cheating in weights and percentage loss on cost price. Many shopkeepers in aptitude problems use less quantity than they claim in order to gain extra profit even while pretending to give a discount or incur a loss. You must track both the quantity sold and the quoted loss percentage to find the true profit or loss. Given Data / Assumptions: Seller charges for 1 kg but actually gives only 840 g. He claims to sell at 4% loss on cost price. We assume cost price is per kilogram of goods. We need to calculate the true percentage profit or loss. Concept / Approach: The trick is to compare what the seller receives (selling price for 1 kg) with what it actually costs him (cost of 840 g). First, assume a convenient cost price for 1 kg, say Rs 100. Then use the claimed 4% loss to find the selling price for 1 kg. Since he really gives only 840 g for this price, his effective cost for that quantity is less, leading to profit. Finally compute actual profit% on the cost of 840 g. Step-by-Step Solution: Step 1: Assume cost price of 1 kg = Rs 100.Step 2: With a 4% loss, selling price for 1 kg (as claimed) SP = 0.96 * 100 = Rs 96.Step 3: In reality, when he charges Rs 96, he gives only 840 g. So actual cost to him for 840 g = (840 / 1000) * 100 = Rs 84.Step 4: Actual profit for 840 g = SP - actual CP = 96 - 84 = Rs 12.Step 5: Actual profit% = (12 / 84) * 100 = 14.2857% ≈ 14.28% profit. Verification / Alternative check: You may choose any other convenient cost price, such as Rs 50 per kg. Then SP = 0.96 * 50 = Rs 48 and cost of 840 g = 0.84 * 50 = Rs 42. Profit = 48 - 42 = Rs 6, and profit% = (6 / 42) * 100 = 14.2857%, giving the same result. This proves that the percentage profit is independent of the assumed base cost price. Why Other Options Are Wrong: 24.18 % profit or loss and 14.28 % loss result from wrongly treating the loss as genuine and ignoring the cheating in weight, or from using 1 kg repeatedly without scaling down to 840 g. The sign must be profit, not loss, because the seller receives more money than the true cost of the goods he actually hands over. Common Pitfalls: Many learners simply apply 4% loss on cost and stop, taking it as the final answer. Others compute profit% using 96 and 100 directly without adjusting for the short weight. Always remember that if the quantity given to the customer is less than what is charged for, you must first find the cost of the smaller quantity and then compare with the selling price. This is the only way to get the true profit or loss percentage. Final Answer: The seller is actually making a profit of about 14.28 % profit on his goods.

Question 19

A driver of an auto rickshaw makes a profit of 20% on every trip when he carries 3 passengers and the petrol price is Rs 30 per litre. For the same journey, if he carries 4 passengers per trip and the petrol price falls to Rs 24 per litre, what perc…

Accepted Answer

Introduction / Context: This question tests combined reasoning with profit, cost and proportional changes in price and number of passengers. The auto rickshaw driver earns profit from passenger fares while spending money on petrol and other fixed expenses. When the petrol price changes and the number of passengers changes, the profitability of each trip also changes. We need to quantify this change in terms of profit percentage. Given Data / Assumptions: With 3 passengers and petrol at Rs 30 per litre, profit per trip is 20%. For the same journey, he later carries 4 passengers. Petrol price falls from Rs 30 to Rs 24 per litre (a 20% reduction). Other expenses per trip such as maintenance and driver time remain constant. Assume the fare charged per passenger for the trip remains unchanged. Concept / Approach: We assume that the entire variable cost is petrol, so when petrol price falls by 20%, total trip cost falls by 20%. Let fare per passenger be R. We can then express cost and revenue algebraically for both scenarios. Once we have new revenue and new cost in terms of R, we compute profit% = (profit / cost) * 100. Using algebra with a dummy variable keeps the solution general and clear. Step-by-Step Solution: Step 1: Let fare per passenger = R. For 3 passengers, revenue SP₁ = 3R.Step 2: Profit is 20%, so cost C₁ satisfies SP₁ = 1.2 * C₁ ⇒ 3R = 1.2 * C₁ ⇒ C₁ = 3R / 1.2 = 2.5R.Step 3: Petrol price falls by 20%, so new cost C₂ = 0.8 * C₁ = 0.8 * 2.5R = 2R (assuming cost is dominated by petrol).Step 4: With 4 passengers at same fare, new revenue SP₂ = 4R.Step 5: New profit = SP₂ - C₂ = 4R - 2R = 2R, so profit% = (2R / 2R) * 100 = 100%. Verification / Alternative check: You may take a concrete value, for example R = Rs 100. Then initially SP₁ = Rs 300 and C₁ = Rs 250, giving 20% profit. After the change, C₂ = Rs 200 and SP₂ = Rs 400, making profit = Rs 200. The profit percentage is (200 / 200) * 100 = 100%. This confirms the algebraic solution and shows that the profit has doubled relative to cost. Why Other Options Are Wrong: 68%, 80% and 75% might appear realistic but they all underestimate the strong effect of both reduced petrol price and an extra passenger. When you work out the precise algebra, only 100% fits the combined impact of reduced cost and increased revenue. The other values come from partial adjustments or from incorrectly assuming that only one variable (either passengers or petrol price) changes. Common Pitfalls: One common error is to treat profit percentage as directly proportional to the number of passengers, ignoring the change in cost. Another is to reduce selling price proportionally with petrol price instead of keeping the fare per passenger fixed. Carefully separating revenue and cost, and writing explicit equations, helps avoid these mistakes in multi-factor percentage questions. Final Answer: After carrying 4 passengers and with a reduced petrol price, the driver earns a profit of 100% on the cost of the journey.

Question 20

Three varieties of mangoes, M, N and O, have cost prices Rs 20 per kg, Rs 40 per kg and Rs 50 per kg respectively. They are mixed in the ratio 2 : 3 : 5 to form a 1 kg mixture. At what selling price per kg should the mixture be sold to earn an overa…

Accepted Answer

Introduction / Context: Mixture problems with profit and loss are very popular in quantitative aptitude. Here, three types of mangoes have different cost prices and are mixed in a fixed ratio. We must first compute the average cost of the mixture per kilogram and then add a desired profit percentage to find the selling price. This teaches how weighted averages and profit percentages work together. Given Data / Assumptions: Type M costs Rs 20 per kg. Type N costs Rs 40 per kg. Type O costs Rs 50 per kg. They are mixed in the ratio M : N : O = 2 : 3 : 5. Required profit on the mixture = 20% over cost. We need selling price per kg of the final mixture. Concept / Approach: Because the mixture is in the ratio 2 : 3 : 5, we can assume a convenient total weight, say 10 kg (2 + 3 + 5). We then compute the total cost for these 10 kg, divide by 10 to find cost per kg, and finally multiply by 1.2 to account for a 20% profit. This method uses the idea of weighted average and ensures all three varieties are correctly included in the cost. Step-by-Step Solution: Step 1: Assume total mixture = 2 + 3 + 5 = 10 kg.Step 2: Cost of M in the mixture = 2 kg * Rs 20/kg = Rs 40.Step 3: Cost of N in the mixture = 3 kg * Rs 40/kg = Rs 120.Step 4: Cost of O in the mixture = 5 kg * Rs 50/kg = Rs 250.Step 5: Total cost for 10 kg = 40 + 120 + 250 = Rs 410, so cost per kg = 410 / 10 = Rs 41.Step 6: To earn 20% profit, SP per kg = 41 * 1.2 = Rs 49.2. Verification / Alternative check: If 10 kg of mixture cost Rs 410, then selling 10 kg at Rs 49.2 per kg gives revenue of 10 * 49.2 = Rs 492. Profit = 492 - 410 = Rs 82. Profit percentage = (82 / 410) * 100 = 20%. This matches the required profit and confirms both the average cost and final selling price per kg are correct. Why Other Options Are Wrong: Rs 47, Rs 48.5 and Rs 50.3 correspond to profit percentages different from 20%. Some may give less than 20%, others more. For instance, selling at Rs 47 would clearly yield a profit of only (47 - 41)/41 ≈ 14.63%. Selling at Rs 50.3 gives a profit of about 22.8%. Therefore, only Rs 49.2 satisfies the 20% profit condition exactly. Common Pitfalls: Common mistakes include taking the simple average of 20, 40 and 50 without weighting them by the ratio, or misinterpreting 20% profit as 20 rupees added. Another frequent error is to compute the profit percentage on selling price instead of cost price. Always use a weighted average for mixtures and then apply profit, profit% = (SP - CP) / CP * 100. Final Answer: The shopkeeper should sell the mango mixture at Rs. 49.2 per kg to earn a 20% profit.

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