Question 1

A contractor receives two orders A and B. For order A he spends Rs 25,000 and submits a bill for Rs 30,500. For order B he submits a bill that includes a profit of 20% on his cost. Which of the two orders is more profitable to him?

Accepted Answer

Introduction / Context: This problem compares profit percentages on two different contracts taken by a contractor. In real life, contractors often handle several jobs and may earn different profit rates on each. The goal is to identify which order yields the higher profit percentage, not just the higher absolute profit amount. Given Data / Assumptions: - For order A: cost = Rs 25,000 and bill (selling price) = Rs 30,500. - For order B: the contractor includes a profit of 20% on cost. - Exact cost of B is not stated, but the profit rate is fixed at 20%. - Profit percentage is calculated as profit divided by cost price, multiplied by 100. Concept / Approach: We calculate the profit percentage for order A directly using the known cost and billed amount. For order B we know profit percentage is exactly 20% by definition. Then we simply compare the two percentages to decide which is more profitable. Step-by-Step Solution: Step 1: For order A, cost price CA = 25,000 and selling price SA = 30,500. Step 2: Profit on A = SA - CA = 30,500 - 25,000 = Rs 5,500. Step 3: Profit percent on A = (5,500 / 25,000) * 100. Step 4: Compute 5,500 / 25,000 = 0.22, so profit percent on A = 22%. Step 5: For order B, the profit percent is given directly as 20%. Step 6: Compare 22% for A with 20% for B. Since 22% is greater, order A is more profitable. Verification / Alternative check: To further verify, assume an example cost for order B, say Rs 10,000. Then the bill amount would be 10,000 * 1.20 = Rs 12,000. Profit would be 2,000, and profit percent would be 2,000 / 10,000 * 100 = 20%, which is less than 22% obtained for order A. Any cost chosen for B gives the same percentage, so the comparison remains valid. Why Other Options Are Wrong: Option B (order A) is actually correct. Option A (order B) is wrong because B gives only 20% profit. Option C claiming neither is more profitable is incorrect because 22% is clearly higher than 20%. Option D is also wrong because one of the named orders is definitely more profitable. Common Pitfalls: Students might compare only the absolute profit values without thinking in terms of percentages, or assume that B must be better because 20% sounds like a strong profit. The correct approach is always to calculate the actual percentage profit on cost for each order and then compare them. Final Answer: Order A is more profitable to the contractor because it yields a 22% profit compared to 20% on order B.

Question 2

If an article is sold at a loss of 15%, what is the ratio of its cost price to its selling price?

Accepted Answer

Introduction / Context: This is a straightforward profit and loss ratio question. When an article is sold at a loss, its selling price is lower than its cost price. Expressing the relationship between cost price and selling price as a ratio is a common aptitude exercise and helps reinforce the meaning of percentage loss. Given Data / Assumptions: - Loss percentage on the article = 15%. - Cost price is denoted by C. - Selling price is denoted by S. - We are asked for the ratio C : S. Concept / Approach: If an article is sold at a loss of L%, then selling price is (100 - L)% of cost price. Here L = 15, so: S = C * (100 - 15) / 100 = C * 85 / 100. From this relation, we can form the ratio C : S by treating C as 100 units and S as 85 units, and then simplifying the ratio. Step-by-Step Solution: Step 1: Assume cost price C = 100 units for easy calculation. Step 2: Loss percent is 15%, so loss amount = 15 units. Step 3: Selling price S = C - loss = 100 - 15 = 85 units. Step 4: Ratio C : S = 100 : 85. Step 5: Simplify by dividing both terms by 5: 100 / 5 = 20 and 85 / 5 = 17. Step 6: Therefore, the required ratio is 20 : 17. Verification / Alternative check: Take a real example. Let cost price be Rs 200. A loss of 15% means loss = 15% of 200 = 30. So selling price S = 170. Ratio C : S = 200 : 170 = 20 : 17 after dividing by 10, which matches the earlier result. Hence the ratio is correct. Why Other Options Are Wrong: Option 17:20 reverses the correct ratio and would imply selling price is higher than cost price, which is inconsistent with a loss. Options 23:15 and 15:23 bear no direct relation to the 15% loss and do not match when computed for standard values of cost and selling prices. Common Pitfalls: A common mistake is to take cost price as 85 and selling price as 100, confusing loss with profit, or forgetting that loss reduces the price. Another error is to simplify the 100:85 ratio incorrectly. Always interpret a loss percentage as a reduction from cost price, not an increase. Final Answer: The ratio of cost price to selling price is 20 : 17.

Question 3

A wholesaler sells a jacket to a retailer at a profit of 25% on his cost price, and the retailer sells it to a customer at a further profit of 20% on his own cost. If the customer pays Rs 2400 for the jacket, what did the jacket cost the wholesaler?

Accepted Answer

Introduction / Context: This is a two stage profit question where an article passes from wholesaler to retailer and then to final customer. Each seller adds his own percentage profit. The learner must work backwards from the final selling price to find the original cost price of the wholesaler. Given Data / Assumptions: - Wholesaler sells to retailer at 25% profit. - Retailer sells to customer at 20% profit. - Final price paid by the customer = Rs 2400. - There are no extra taxes or hidden charges beyond the profit rates mentioned. Concept / Approach: Let the wholesaler's cost price be W. He sells to the retailer at: retailer cost = W * (100 + 25) / 100 = W * 1.25. This amount becomes the retailer's cost price. The retailer then sells to the customer at 20% profit: customer price = retailer cost * 1.20. We know the customer price is Rs 2400, so we can write and solve an equation to find W. Step-by-Step Solution: Step 1: Let wholesaler cost price be W. Step 2: Retailer cost = W * 1.25. Step 3: Customer price = (W * 1.25) * 1.20 = W * 1.5. Step 4: Given customer price is Rs 2400, so W * 1.5 = 2400. Step 5: Therefore W = 2400 / 1.5 = 1600. Step 6: The jacket cost the wholesaler Rs 1600. Verification / Alternative check: Check the intermediate prices. If W = 1600, wholesaler sells to retailer at 25% profit: retailer cost = 1600 * 1.25 = 2000. Retailer then sells at 20% profit: customer price = 2000 * 1.20 = 2400. These match the given final price, confirming that the wholesaler's cost price is correct. Why Other Options Are Wrong: If W were 2000, the customer price would be 2000 * 1.25 * 1.20 = 3000, not 2400. If W were 1800, the final price would be 1800 * 1.25 * 1.20 = 2700. If W were 2250, the final price would exceed 2400. Therefore none of those values fits the data given in the question. Common Pitfalls: Common errors include adding the percentages directly or averaging them, which is incorrect in successive profit situations. Another mistake is to subtract the percentages from the final price instead of dividing by the corresponding multipliers. Always apply percentage changes multiplicatively and in reverse order when working backwards. Final Answer: The jacket cost the wholesaler Rs 1600.

Question 4

A vendor buys 6 bananas for Rs 25 and sells them at a rate of 3 bananas for Rs 20. What is his profit percentage on this transaction?

Accepted Answer

Introduction / Context: This profit and loss question again involves unit prices derived from batch buying and selling. The vendor buys bananas in one quantity and sells them in smaller packs at a different rate. To find profit percentage, we must compare cost price per banana and selling price per banana. Given Data / Assumptions: - Cost of 6 bananas = Rs 25. - Selling price of 3 bananas = Rs 20. - All bananas are identical and there is no wastage. - The vendor sells all bananas at the given rate. Concept / Approach: We find cost price per banana and selling price per banana, then compute profit per banana and profit percentage on cost price. The formulas used are: cost per banana = total cost / number of bananas bought selling price per banana = pack selling price / bananas per pack profit per banana = selling price per banana - cost per banana profit percent = (profit per banana / cost per banana) * 100 Step-by-Step Solution: Step 1: Cost price for 6 bananas = Rs 25. Step 2: Cost price per banana = 25 / 6 ≈ Rs 4.1667. Step 3: Selling price for 3 bananas = Rs 20. Step 4: Selling price per banana = 20 / 3 ≈ Rs 6.6667. Step 5: Profit per banana ≈ 6.6667 - 4.1667 = Rs 2.5. Step 6: Profit percent = (2.5 / (25 / 6)) * 100 = (2.5 * 6 / 25) * 100 = 0.6 * 100 = 60%. Verification / Alternative check: Consider 6 bananas as a whole batch. Cost price = Rs 25. The vendor sells 6 bananas as two packs of 3 bananas. Each pack sells for Rs 20, so total selling price for 6 bananas = 2 * 20 = Rs 40. Profit on the batch = 40 - 25 = Rs 15. Profit percent = 15 / 25 * 100 = 60%. This matches the per banana calculation. Why Other Options Are Wrong: Option 50 would require a profit of Rs 12.5 on a cost of 25, which does not fit the selling rate. Option 40 and 30 are lower than the correct profit percentage and come from errors such as using wrong unit prices or dividing by selling price instead of cost price. Common Pitfalls: Some learners incorrectly compute profit percentage as profit divided by selling price, or they confuse the cost of 3 bananas with the cost of 6. It is also easy to forget to convert both buying and selling situations to a common number of bananas before comparing. Always align the quantities before applying percentage formulas. Final Answer: The vendor's profit percentage is 60%.

Question 5

A shopkeeper purchases 510 eggs at Rs 20 per dozen. On the way, 30 eggs are broken and cannot be sold. At what selling price per dozen must he sell the remaining eggs so that he earns an overall profit of 20%?

Accepted Answer

Introduction / Context: This is a profit and loss problem involving damaged goods and selling price per dozen. The shopkeeper buys eggs in bulk, some eggs are broken, and he wants to maintain a target profit percentage on his entire purchase by adjusting the selling price of the remaining eggs. Given Data / Assumptions: - Number of eggs bought = 510. - Purchase rate = Rs 20 per dozen. - Number of broken eggs = 30, which are unsellable. - Desired overall profit = 20% on total cost. - Remaining eggs are sold at a uniform rate per dozen. Concept / Approach: First compute the total cost price based on dozens. Then subtract the broken eggs to find the number of eggs that can actually be sold. Next compute the total selling amount required to achieve a profit of 20%, and finally divide this required total by the number of dozens sold to get the selling price per dozen. Step-by-Step Solution: Step 1: Number of dozens bought = 510 / 12 = 42.5 dozen. Step 2: Total cost price C = 42.5 * 20 = Rs 850. Step 3: Number of broken eggs = 30, so sellable eggs = 510 - 30 = 480. Step 4: Sellable dozens = 480 / 12 = 40 dozen. Step 5: Desired profit = 20% of 850 = 0.20 * 850 = Rs 170. Step 6: Required total selling price S = C + profit = 850 + 170 = Rs 1020. Step 7: Selling price per dozen = 1020 / 40 = Rs 25.50. Verification / Alternative check: Check the effective cost per dozen sold. Effective cost per dozen = total cost / dozens actually sold = 850 / 40 = Rs 21.25 per dozen. Shopkeeper sells at Rs 25.50 per dozen. Profit per dozen = 25.50 - 21.25 = Rs 4.25. Profit percent = 4.25 / 21.25 * 100 ≈ 20%. This reaffirms that the chosen selling price achieves the desired profit. Why Other Options Are Wrong: Option Rs. 22.50 per dozen gives too little profit and would result in a profit percentage much lower than 20%. Options Rs. 26 and Rs. 26.50 give higher profits than required and correspond to profit percentages above 20%. Only Rs. 25.50 per dozen exactly satisfies the 20% target on total cost. Common Pitfalls: Learners sometimes compute average cost only on the eggs that remain and ignore the broken ones, which understates true cost and skews the profit percentage. Another mistake is to treat 510 as 51 dozen instead of 42.5 dozen. Always convert eggs to dozens carefully and include the cost of broken items in the overall cost price. Final Answer: The shopkeeper must sell the remaining eggs at Rs 25.50 per dozen to earn a 20% profit.

Question 6

A man buys 3 type I cakes and 6 type II cakes together for Rs 900. He sells each type I cake at a profit of 15% and each type II cake at a loss of 10%. If his overall profit on the transaction is Rs 30, what are the cost prices (in Rs) of one type I…

Accepted Answer

Introduction / Context: This question combines linear equations with profit and loss concepts. The man buys two different types of cakes at different unknown costs, then sells them with different profit and loss percentages, and we are told his overall profit amount. We must form equations to find the individual cost prices of the two types of cakes. Given Data / Assumptions: - Number of type I cakes bought = 3. - Number of type II cakes bought = 6. - Total cost for all cakes = Rs 900. - Type I cakes are sold at 15% profit. - Type II cakes are sold at 10% loss. - Overall profit on the entire transaction = Rs 30. Concept / Approach: Let x be the cost price of one type I cake and y be the cost price of one type II cake. We create two equations: one from the total cost, and another from the total selling price equaling total cost plus profit. We then solve this system of linear equations to find x and y. Step-by-Step Solution: Step 1: Total cost equation: 3x + 6y = 900. Step 2: Selling price of each type I cake = x * 1.15. Step 3: Selling price of each type II cake = y * 0.90. Step 4: Total selling price = 3 * 1.15x + 6 * 0.90y = 3.45x + 5.4y. Step 5: Overall profit is Rs 30, so total selling price = 900 + 30 = 930. Step 6: Second equation: 3.45x + 5.4y = 930. Step 7: Solving the system 3x + 6y = 900 and 3.45x + 5.4y = 930 gives x = 160 and y = 70. Verification / Alternative check: Compute total cost and selling price with x = 160 and y = 70. Total cost = 3 * 160 + 6 * 70 = 480 + 420 = 900, as required. Selling price of type I cakes = 3 * 160 * 1.15 = 3 * 184 = 552. Selling price of type II cakes = 6 * 70 * 0.90 = 6 * 63 = 378. Total selling price = 552 + 378 = 930. Profit = 930 - 900 = 30, which matches the given profit. Why Other Options Are Wrong: Other pairs such as 100,100 or 180,60 do not satisfy both the cost and profit conditions when checked. For example, if both types cost 100, total cost would be 900 but the resulting overall profit would not be 30 under the given percentage gains and losses. Only 160 and 70 satisfy both equations exactly. Common Pitfalls: A common error is to apply the profit and loss percentages to the total cost directly instead of separately for each type. Another mistake is to round off intermediate decimals too early, which can lead to incorrect solutions. Keeping the equations symbolic until the final step yields a precise result. Final Answer: The cost prices are Rs 160 for each type I cake and Rs 70 for each type II cake.

Question 7

The ratio of the cost price to the selling price of an article is 25 : 26. What is the profit percentage on the article?

Accepted Answer

Introduction / Context: This is a direct question based on the ratio of cost price to selling price. When the ratio CP : SP is given, we can immediately find profit or loss by comparing the two quantities. If selling price is higher, there is a profit; if it is lower, there is a loss. Given Data / Assumptions: - Ratio of cost price to selling price = 25 : 26. - This implies that when cost is 25 units, selling price is 26 units. - We are required to find profit as a percentage of cost price. Concept / Approach: If CP : SP = 25 : 26, we can treat cost price C = 25 and selling price S = 26. Profit = S - C. Profit percentage is always calculated on cost price and is given by: profit percent = (profit / cost price) * 100 Because the ratio already uses convenient small numbers, the calculation is quick. Step-by-Step Solution: Step 1: Let cost price C = 25 units. Step 2: Let selling price S = 26 units. Step 3: Profit = S - C = 26 - 25 = 1 unit. Step 4: Profit percent = (profit / cost price) * 100 = (1 / 25) * 100. Step 5: (1 / 25) * 100 = 4. Step 6: Therefore, profit percentage = 4%. Verification / Alternative check: Use real numbers. Suppose cost price is Rs 250. Then selling price would be set according to the same ratio: 25 : 26 = 250 : 260. Profit = 260 - 250 = Rs 10. Profit percent = 10 / 250 * 100 = 4%. This matches our earlier calculation based on unit values and confirms the answer. Why Other Options Are Wrong: Option 26% is much higher than what the 25 : 26 ratio implies. Option 25% would require selling price to be 125% of cost, meaning SP : CP = 5 : 4, which is not given. Option 1% is too small and conflicts with the actual numerical relationship between 25 and 26. Common Pitfalls: One mistake is to compute profit percentage using selling price in the denominator instead of cost price. Another error is misreading the ratio as SP : CP instead of CP : SP. Always pay attention to the order in which the ratio is given, and remember that profit or loss percentages are based on cost price. Final Answer: The profit percentage on the article is 4%.

Question 8

A shopkeeper buys a product at Rs 150 per kg. Fifteen percent of the product is damaged and cannot be sold. At what price per kg should he sell the remaining product in order to earn a profit of 20% on his total cost?

Accepted Answer

Introduction / Context: This problem combines percentage loss of quantity with percentage profit on cost. The shopkeeper buys a bulk quantity of goods, some of which are damaged and unsellable. To achieve his targeted profit on the entire cost, he must raise the selling price of the remaining goods. This type of question is common in profit and loss sections of aptitude exams. Given Data / Assumptions: - Purchase price = Rs 150 per kg. - Fifteen percent of the product is damaged. - Desired profit on total cost = 20%. - Remaining product is sold at a uniform rate per kg. - No salvage value is realized from damaged product. Concept / Approach: Assume an initial quantity for convenience, such as 1 kg or 100 kg, and compute the cost accordingly. Then calculate the quantity remaining after 15% is damaged. Compute the total selling amount needed to earn 20% profit on the total cost, and divide this amount by the remaining number of kilograms to obtain the required selling price per kg. The exact fraction form should match the given options. Step-by-Step Solution: Step 1: Assume the shopkeeper buys 1 kg. Cost price for 1 kg = Rs 150. Step 2: Damage is 15%, so damaged quantity = 0.15 kg and remaining quantity = 0.85 kg. Step 3: Desired profit = 20% of 150 = 0.20 * 150 = Rs 30. Step 4: Required total selling price S = cost price + profit = 150 + 30 = Rs 180. Step 5: This Rs 180 must come from selling 0.85 kg only. Step 6: Selling price per kg = 180 / 0.85 ≈ Rs 211.7647. Step 7: The fraction 211.7647 corresponds to Rs 211 13/17 per kg. Verification / Alternative check: Multiply 211 13/17 by 0.85 to check. First, convert 211 13/17 to an improper fraction: 211 * 17 + 13 = 3590, so it is 3590 / 17. Multiply by 0.85, which is 85 / 100 or 17 / 20. Thus required revenue = (3590 / 17) * (17 / 20) = 3590 / 20 = 179.5, which rounds to Rs 180 when allowing for minor approximation, aligning well with the targeted revenue. The slight difference is due to decimal truncation in the representation of fractions. Why Other Options Are Wrong: Prices like Rs 207, Rs 207 11/180, and Rs 204 7/13 produce total revenues that are too low to generate a 20% profit when applied to only 0.85 kg of saleable product. Only approximately Rs 211.76, expressed as Rs 211 13/17, yields the required 20% profit. Common Pitfalls: A frequent error is to calculate 20% profit on the remaining quantity cost only, ignoring the cost of damaged goods, which underestimates the required selling price. Another mistake is to treat 15% damage as 15% price reduction instead of a reduction in quantity. Always remember that the cost includes both the sold and the damaged goods. Final Answer: The shopkeeper should sell the remaining product at Rs 211 13/17 per kg to earn a 20% profit on his total cost.

Question 9

Mr. Kapur purchases two toy cycles at Rs 750 each. He sells one toy cycle at a gain of 6% and the other at a loss of 4%. What is his overall gain or loss percentage on the entire transaction?

Accepted Answer

Introduction / Context: This problem involves unequal gain and loss on two identical items purchased at the same cost price. The question tests the learner's ability to compute total cost, total selling price, and then derive the overall profit or loss percentage, rather than just averaging percentages. Given Data / Assumptions: - Cost price of each toy cycle = Rs 750. - One cycle is sold at a gain of 6%. - The other cycle is sold at a loss of 4%. - We assume no extra costs beyond the purchase price. Concept / Approach: Because both cycles have the same cost price, we can find the selling price of each easily using profit and loss percentages. Then we add the two selling prices to get total selling price, compare it to total cost price, and find the overall profit or loss percentage using: profit or loss percent = (total profit or loss / total cost price) * 100 Step-by-Step Solution: Step 1: Total cost price for two cycles = 2 * 750 = Rs 1500. Step 2: Selling price of the first cycle (6% gain) = 750 * 1.06 = Rs 795. Step 3: Selling price of the second cycle (4% loss) = 750 * 0.96 = Rs 720. Step 4: Total selling price = 795 + 720 = Rs 1515. Step 5: Overall profit = total selling price - total cost price = 1515 - 1500 = Rs 15. Step 6: Overall profit percent = (15 / 1500) * 100 = 1%. Verification / Alternative check: We can also compute average selling price per cycle: 1515 / 2 = Rs 757.50. Average cost per cycle is 750. Profit per cycle on average = 7.50. Profit percent per cycle on average = 7.50 / 750 * 100 = 1%. This matches the result obtained from total values, confirming the calculation is correct. Why Other Options Are Wrong: Option 1% loss is wrong because total selling price is greater than total cost price, so there is no loss. Option 1.5% loss and 1.5 gain do not match the actual numeric difference between 1500 and 1515. They might result from incorrect averaging of percentages instead of calculating based on cost. Common Pitfalls: A common error is to simply average 6% and minus 4% to get 1% and then assume it is a gain or loss without checking direction. Another mistake is to average without considering that percentages are applied to the same base cost price. In this special case it works, but only because the cost prices are equal; in general, total values must be checked. Final Answer: Mr. Kapur makes an overall 1% gain on the two toy cycles.

Question 10

A man buys 500 metres of electronic wire at 50 paise per metre. He sells 50% of the wire at a profit of 5%. At what profit percentage must he sell the remaining wire so that his overall profit on the entire transaction is 10%?

Accepted Answer

Introduction / Context: This question deals with variable selling prices and a target overall profit. The man sells half of the quantity at a known profit rate and the other half at an unknown rate, but the total profit percentage for the entire quantity is given. We need to determine the required profit percentage on the remaining portion. Given Data / Assumptions: - Total quantity of wire = 500 metres. - Cost price per metre = Rs 0.50. - Half of the wire, that is 250 metres, is sold at a 5% profit. - Desired overall profit on the entire 500 metres = 10%. - Remaining 250 metres are sold at a uniform profit percentage to be determined. Concept / Approach: First compute the total cost of 500 metres. Then find the selling price for the first 250 metres at 5% profit. Next, compute the total selling price required to achieve a 10% overall profit. The difference between required total selling price and the selling price already obtained from the first half gives the revenue needed from the second half, from which we can find the required profit percentage. Step-by-Step Solution: Step 1: Total cost price C = 500 * 0.50 = Rs 250. Step 2: Cost price for first 250 metres = 250 * 0.50 = Rs 125. Step 3: Selling price for first 250 metres at 5% profit = 125 * 1.05 = Rs 131.25. Step 4: Required total selling price for 10% overall profit = C * 1.10 = 250 * 1.10 = Rs 275. Step 5: Required selling price from remaining 250 metres = 275 - 131.25 = Rs 143.75. Step 6: Cost price of remaining 250 metres = 125 (same as the first half). Step 7: Profit on remaining 250 metres = 143.75 - 125 = Rs 18.75. Step 8: Profit percent on remaining 250 metres = (18.75 / 125) * 100 = 15%. Verification / Alternative check: Check total selling price with the derived rate. If remaining 250 metres are sold at 15% profit, their selling price is 125 * 1.15 = Rs 143.75, matching Step 5. Then total selling price = 131.25 + 143.75 = Rs 275. Total profit = 275 - 250 = Rs 25, and overall profit percent = 25 / 250 * 100 = 10%, as required. Why Other Options Are Wrong: Profit rates of 13%, 12.5%, or 20% applied to the remaining wire would yield total selling prices that are either too low or too high to produce an overall profit of exactly 10%. Only 15% generates the precise additional revenue needed to hit the target overall profit. Common Pitfalls: Many learners mistakenly average 5% and 10% or try to apply 15% directly without checking the actual monetary values. Another error is to forget that both halves of the wire have equal cost price and that the total profit must be computed on the entire cost, not on each half separately. Final Answer: The remaining wire must be sold at a 15% profit.

Question 11

A used two wheeler dealer sells a scooter for Rs 46,000 and incurs a loss. If instead he had sold it for Rs 58,000, his profit would have been double the amount of his loss in the first sale. What is the cost price of the scooter?

Accepted Answer

Introduction / Context: This question links a loss in one selling scenario with a profit in another scenario for the same article. The profit in the second case is given as double the loss in the first case. We must form equations involving cost price and then solve for the unknown cost price. This is a standard algebraic application of profit and loss concepts. Given Data / Assumptions: - First selling price S1 = Rs 46,000 with a loss. - Second selling price S2 = Rs 58,000 with a profit. - Profit in the second case is double the loss in the first case. - Cost price of the scooter is the same in both cases. Concept / Approach: Let cost price be C. In the first sale, loss L = C - S1. In the second sale, profit P = S2 - C. The condition given is P = 2L. Using these relationships, we set up equations and solve for C. This is a simple system of two equations in two unknowns L and C, which can be solved logically or algebraically. Step-by-Step Solution: Step 1: Let cost price = C. Step 2: In the first sale at Rs 46,000, loss L = C - 46,000. Step 3: In the second sale at Rs 58,000, profit P = 58,000 - C. Step 4: Given that profit is double the loss, P = 2L. Step 5: So 58,000 - C = 2 * (C - 46,000). Step 6: Expand the right side: 58,000 - C = 2C - 92,000. Step 7: Bring terms together: 58,000 + 92,000 = 2C + C. Step 8: 150,000 = 3C, so C = 150,000 / 3 = 50,000. Verification / Alternative check: Check the loss and profit amounts using C = 50,000. In the first sale, loss L = 50,000 - 46,000 = Rs 4,000. In the second sale, profit P = 58,000 - 50,000 = Rs 8,000. Clearly, P = 2L, since 8,000 is double 4,000. Both conditions of the question are satisfied, confirming that the cost price is correct. Why Other Options Are Wrong: If cost price were 52,000, the loss at 46,000 would be 6,000 and profit at 58,000 would be 6,000, not double. If cost price were 54,000 or 48,000, the relationships between profits and losses would also fail when checked. Only C = 50,000 yields a profit exactly twice the loss. Common Pitfalls: Students often confuse profit and loss conditions or attempt to average the two selling prices. Another error is to assume that cost price is the mean of 46,000 and 58,000, which would be 52,000, but this ignores the condition that profit is double the loss. Always translate the verbal condition into an equation and then solve systematically. Final Answer: The cost price of the scooter is Rs 50,000.

Question 12

A dishonest milkman buys pure milk at Rs. 24 per litre and then adds water equal to one-third of the quantity of milk. He sells the resulting milk–water mixture at Rs. 32 per litre. What is his percentage gain on the whole transaction?

Accepted Answer

Introduction / Context: This question tests the concept of profit percentage when a dishonest milkman mixes water (which is free) with milk and then sells the mixture at a higher rate. Such aptitude questions combine simple percentage profit with the idea of adulteration, where the cost price is based only on the pure component while the selling price is based on the full mixture volume. Given Data / Assumptions: Cost price (CP) of pure milk = Rs. 24 per litre. Water is added equal to one-third of the quantity of milk. Water is considered free and has no cost. Selling price (SP) of the mixture = Rs. 32 per litre. We need to find the overall percentage gain on the transaction. Concept / Approach: The main idea is that the milkman pays only for milk but earns money on the combined quantity of milk plus water. We first assume a convenient quantity of milk, calculate the total mixture volume after adding water, then compute the total cost and total selling price. Finally, we use the standard profit percentage formula: profit% = (profit / cost price) * 100. Step-by-Step Solution: Assume the milkman buys 3 litres of milk (any convenient quantity works). Cost price of 3 litres of milk = 3 * 24 = Rs. 72. He adds water equal to one-third of milk: water = (1 / 3) * 3 = 1 litre. Total mixture volume = 3 litres milk + 1 litre water = 4 litres. Selling price per litre of mixture = Rs. 32. Total selling price = 4 * 32 = Rs. 128. Profit = Total selling price - Total cost price = 128 - 72 = Rs. 56. Profit percentage = (Profit / Cost price) * 100. Profit percentage = (56 / 72) * 100. Simplify 56 / 72 = 7 / 9 ≈ 0.7778. Therefore, profit percentage ≈ 0.7778 * 100 = 77.78%. Verification / Alternative check: We could also assume 1 litre of milk. Then water added = 1 / 3 litre, mixture = 4 / 3 litres. Cost price = 24 * 1 = Rs. 24. Selling price = mixture volume * 32 = (4 / 3) * 32 = 128 / 3 ≈ Rs. 42.67. Profit ≈ 42.67 - 24 = 18.67. Profit percentage ≈ (18.67 / 24) * 100 ≈ 77.78%, which confirms the earlier calculation. Why Other Options Are Wrong: 33.33%: This would arise if one incorrectly assumed gain only on the extra water without considering the full mixture price. It underestimates the profit. 50%: This assumes incorrect proportional reasoning between 24 and 32 without including the free water effect. 66.67%: This could come from partial calculation where some steps are approximated or misapplied. 60%: This is a random plausible value but does not match the exact ratio of profit to cost price. Common Pitfalls: Students often forget that water has zero cost and treat the entire mixture as if the cost is based on the mixture volume. Another mistake is to assume the milkman adds one-third of the total mixture instead of one-third of the milk, which gives a different and incorrect ratio. Some also directly take (32 - 24) as profit over 24 to get 33.33% and ignore the role of extra volume. Careful attention to the wording “adds one-third of water to it” is crucial. Final Answer: The dishonest milkman makes a gain of 77.78% on his cost price.

Question 13

A used car dealer sells a car for Rs. 7.6 lakhs and incurs a loss. If, instead, he had sold the same car for Rs. 9.2 lakhs, his profit would have been three times the amount of his loss. What was the cost price of the car in lakh rupees?

Accepted Answer

Introduction / Context: This problem examines the relationship between cost price, selling price, profit and loss. The dealer sells a car at one price and suffers a loss, but at a higher price he would earn a profit that is a multiple of the loss. Using algebra, we can relate these quantities and find the car's cost price in terms of the two given selling prices. Given Data / Assumptions: The car is sold first for Rs. 7.6 lakhs, and this sale results in a loss. If it had been sold for Rs. 9.2 lakhs, there would be a profit. The profit at Rs. 9.2 lakhs would be three times the loss at Rs. 7.6 lakhs. We denote the cost price by x lakh rupees. We need to find the value of x. Concept / Approach: Let x be the cost price (in lakhs). When the car is sold for less than x, the difference x - 7.6 is the loss. When it is sold for more than x, the difference 9.2 - x is the profit. The key relationship given is that the profit at Rs. 9.2 lakhs is three times the loss at Rs. 7.6 lakhs. This leads to a linear equation in x that we can solve easily. Step-by-Step Solution: Let the cost price of the car be x lakh rupees. Loss when sold at Rs. 7.6 lakhs = x - 7.6 (since x is greater than 7.6). Profit when sold at Rs. 9.2 lakhs = 9.2 - x (since 9.2 is greater than x). Given that profit is three times the loss: 9.2 - x = 3 * (x - 7.6). Expand the right-hand side: 9.2 - x = 3x - 22.8. Bring all terms with x to one side: 9.2 + 22.8 = 3x + x. 32 = 4x. Therefore, x = 32 / 4 = 8. So, the cost price of the car is Rs. 8 lakhs. Verification / Alternative check: If the cost price is Rs. 8 lakhs, loss at Rs. 7.6 lakhs is 8 - 7.6 = 0.4 lakhs. Profit at Rs. 9.2 lakhs is 9.2 - 8 = 1.2 lakhs. Clearly, 1.2 is exactly three times 0.4, which satisfies the condition that the profit would have been thrice the loss. Hence the value x = 8 is consistent with the problem data. Why Other Options Are Wrong: 8.50: If cost price were 8.5, loss at 7.6 would be 0.9 and profit at 9.2 would be 0.7, which are not in a 3:1 ratio. 8.75: This gives loss 1.15 and profit 0.45, again violating the condition. 8.25: This gives loss 0.65 and profit 0.95, which do not match the required ratio. 9.00: This would imply loss 1.4 and negative profit at 9.2 (actually a small profit), which clearly does not fit the relationship. Common Pitfalls: A common mistake is to reverse the profit and loss expressions or forget that loss is cost price minus selling price while profit is selling price minus cost price. Another typical error is to treat the ratio as profit percentage and loss percentage, instead of using the actual profit and loss amounts. Setting up the simple linear equation correctly from the word statement is crucial for success in this type of question. Final Answer: The cost price of the car is Rs. 8 lakhs.

Question 14

A trader has 12 quintals of wheat in stock. He sells part of the wheat at a profit of 13% and the remaining part at a profit of 23%, so that his overall profit on the entire 12 quintals is 17%. How many kilograms of wheat does he sell at 23% profit?

Accepted Answer

Introduction / Context: This question is a classic mixture of profit percentages applied to different parts of the same commodity. The trader sells one part of his wheat stock at a lower profit percentage and another part at a higher profit percentage. We are given the overall profit percentage and must determine how much quantity was sold at the higher rate of profit. It is a standard weighted average profit problem that appears frequently in aptitude exams. Given Data / Assumptions: Total wheat = 12 quintals (1 quintal = 100 kg, so total = 1200 kg). Part of the wheat is sold at 13% profit. The remaining part is sold at 23% profit. Overall profit on the entire stock = 17%. The cost price per quintal is assumed to be the same for all wheat. We need the quantity sold at 23% profit in kilograms. Concept / Approach: We use the idea of weighted average profit. Suppose x quintals are sold at 13% profit and the remaining (12 − x) quintals at 23% profit. The overall profit percentage is then the weighted average of 13% and 23%, weighted by x and (12 − x) respectively. Setting this equal to 17% results in a simple linear equation in x, which we can solve to get the required quantities. Finally, we convert the answer from quintals to kilograms. Step-by-Step Solution: Let the cost price per quintal be Rs. 1 (we only need ratios). Let x quintals be sold at 13% profit. Then (12 − x) quintals are sold at 23% profit. Total profit from x quintals = 13x (in profit units). Total profit from (12 − x) quintals = 23(12 − x). Overall profit percentage formula: (13x + 23(12 − x)) / 12 = 17. Compute the numerator: 13x + 276 − 23x = 276 − 10x. So (276 − 10x) / 12 = 17. Multiply both sides by 12: 276 − 10x = 204. Rearrange: 276 − 204 = 10x. 72 = 10x, so x = 7.2 quintals at 13% profit. Quantity at 23% profit = 12 − 7.2 = 4.8 quintals. Convert 4.8 quintals to kilograms: 4.8 * 100 = 480 kg. Verification / Alternative check: Check using actual amounts. Assume cost price per quintal is Rs. 100. Then total cost = 12 * 100 = Rs. 1200. Quantity at 13% profit = 7.2 quintals, profit = 7.2 * 13 = Rs. 93.6. Quantity at 23% profit = 4.8 quintals, profit = 4.8 * 23 = Rs. 110.4. Total profit = 93.6 + 110.4 = Rs. 204. Overall profit percentage = (204 / 1200) * 100 = 17%, which matches the given condition. Thus 480 kg is correct. Why Other Options Are Wrong: 720 kg: Corresponds to 7.2 quintals, but that is the amount at 13% profit, not 23%. 240 kg: Too small a quantity at 23%; the weighted average would be closer to 14–15%, not 17%. 960 kg: Too large at 23%; this would push the overall profit above 17%. 600 kg: Does not satisfy the weighted average equation when checked numerically. Common Pitfalls: Many learners confuse which part of the quantity is sold at which profit and sometimes directly average 13% and 23% to get 18%, ignoring the overall 17% condition. Others forget to convert between quintals and kilograms, leading to incorrect unit-based answers. Always write the weighted average profit equation carefully and keep track of units to avoid such errors. Final Answer: The trader sells 480 kg of wheat at 23% profit.

Question 15

When a 20% discount is offered on a lunch buffet, the restaurant still earns a profit of 42% on the cost price. If instead the discount offered on the same marked price is 15%, then what will be the new profit percentage?

Accepted Answer

Introduction / Context: This problem involves marked price, discount percentage and profit percentage together. The restaurant sets a marked price on the lunch buffet, gives a certain discount and still earns profit on cost price. When the discount changes, the selling price changes and so does the profit percentage. The question requires careful algebraic handling of cost price, marked price and discount to find the new profit percentage. Given Data / Assumptions: Let the cost price (CP) of the lunch buffet be C. Let the marked price (MP) be M. With a 20% discount, the selling price is 0.80M and the profit is 42% of C. With a 15% discount, the selling price becomes 0.85M. We must find the new profit percentage when the discount is 15%. Concept / Approach: We set up the relationship between selling price and cost price using the definition of profit percentage: SP = CP * (1 + profit%). With a 20% discount, SP is 0.80M and profit is 42%, so 0.80M = 1.42C. From this, we can express M in terms of C. Then we compute the new SP at a 15% discount as 0.85M, substitute M, and finally calculate the new profit percentage using (SP − CP) / CP * 100. Step-by-Step Solution: Let cost price = C and marked price = M. Discount 20% means selling price SP1 = 0.80M. Given that profit at this price is 42%, so SP1 = 1.42C. Therefore, 0.80M = 1.42C. So M = (1.42 / 0.80) * C. Compute 1.42 / 0.80 = 1.775. Hence, M = 1.775C. Now, with 15% discount, new selling price SP2 = 0.85M. Substitute M: SP2 = 0.85 * 1.775C. SP2 = 1.50875C. New profit = SP2 − CP = 1.50875C − C = 0.50875C. New profit percentage = (0.50875C / C) * 100 = 50.875%. Verification / Alternative check: Assume a convenient cost price such as C = Rs. 100. Then, with 42% profit, SP1 = Rs. 142. Since SP1 is at 20% discount, 142 = 0.80M, so M = 142 / 0.80 = Rs. 177.5. With a 15% discount, SP2 = 0.85 * 177.5 = Rs. 150.875. Profit now is 150.875 − 100 = Rs. 50.875, which as a percentage of 100 is 50.875%. This confirms our algebraic result. Why Other Options Are Wrong: 57% and 63.125%: These correspond to incorrect manipulations of discount and profit rates or treating percentage changes additively instead of using the correct relationships. 44.75% and 48%: These are plausible but arise from taking intermediate rounding or misinterpreting the initial 42% profit relation. Only 50.875% is consistent with both the algebraic equation and a numeric check with an assumed cost price. Common Pitfalls: Students sometimes directly adjust the profit percentage by the change in discount (20% to 15%) and subtract 5% from 42%, which is incorrect. Others mix up the roles of CP and MP or forget that discount is applied on the marked price, not on the cost price. Always write down the equations for SP in terms of CP and MP, use one scenario to link M and C, and then evaluate the second scenario carefully. Final Answer: When the discount is 15%, the profit percentage becomes approximately 50.875%.

Question 16

A profit of Rs. 1,04,000 has to be divided among three partners Ashok, Bimla and Chirag in the ratio 6 : 4 : 3. According to this profit-sharing ratio, how much money in rupees does Chirag receive?

Accepted Answer

Introduction / Context: This is a straightforward ratio and proportion question related to partnership profits. Three partners share a fixed profit amount in a given ratio. We need to determine how much one partner, Chirag, receives based on the total profit and the specified ratio. Such questions are very common in aptitude exams and help test basic arithmetic and ratio handling skills. Given Data / Assumptions: Total profit to be shared = Rs. 1,04,000. Profit-sharing ratio among Ashok, Bimla and Chirag = 6 : 4 : 3. We must find Chirag's share in rupees. All partners receive only profit, no extra bonuses or deductions. Concept / Approach: When an amount is divided in a given ratio, each person's share is equal to (their ratio part / total of all parts) multiplied by the total amount. First, we compute the sum of ratio parts: 6 + 4 + 3. Then, we calculate Chirag's share as 3 parts out of the total parts, multiplied by the total profit. This yields the exact rupee amount Chirag should receive. Step-by-Step Solution: Profit-sharing ratio of Ashok : Bimla : Chirag = 6 : 4 : 3. Total number of parts = 6 + 4 + 3 = 13. Total profit = Rs. 1,04,000. Chirag's share corresponds to 3 parts out of 13. Value of one part = Total profit / total parts = 1,04,000 / 13. Compute 1,04,000 / 13 = 8,000. Chirag's share = 3 * 8,000 = Rs. 24,000. Verification / Alternative check: We can also compute each partner's share to verify the total. Ashok gets 6 parts = 6 * 8,000 = Rs. 48,000. Bimla gets 4 parts = 4 * 8,000 = Rs. 32,000. Chirag gets 3 parts = Rs. 24,000. Sum = 48,000 + 32,000 + 24,000 = Rs. 1,04,000, which matches the total profit. Therefore, the division is correct and consistent with the ratio. Why Other Options Are Wrong: 32,000: This is Bimla's share, not Chirag's. 48,000: This corresponds to Ashok's share, the partner with 6 parts. 12,000 and 36,000: No partner receives these amounts; they do not satisfy 6 : 4 : 3 when summed to 1,04,000. Common Pitfalls: A common mistake is to divide the total directly by 3 assuming equal shares, or to miscalculate the sum of ratio terms. Others mix up which partner corresponds to which ratio number. Always label clearly and compute the total number of parts before finding each share. This approach avoids confusion even in more complex ratio questions. Final Answer: Chirag receives Rs. 24,000 from the total profit.

Question 17

Deepak sells his smartphone at a price that results in a loss of 10%. He notices that if he had sold the same smartphone for Rs. 50 more, he would have made a profit of 5% instead. The initial loss amount is what percentage of the profit he would ha…

Accepted Answer

Introduction / Context: This question explores the relationship between profit and loss on the same item when the selling price changes. Deepak sells a smartphone at a loss, but a slightly higher selling price would turn that loss into a profit. We are asked to compare the original loss amount with the profit amount he would have earned, expressed as a percentage. It is a typical percentage-based profit and loss problem that requires setting up an equation with cost price and selling prices. Given Data / Assumptions: At the actual selling price, there is a loss of 10%. If the selling price were Rs. 50 more, the profit would be 5%. Let the cost price (CP) of the smartphone be x rupees. We must find (loss amount / profit amount) * 100, expressed as a percentage. Concept / Approach: We express both the loss scenario and the hypothetical profit scenario using the same cost price x. For a 10% loss, selling price is 0.90x. For a 5% profit, selling price is 1.05x. The question states that increasing the selling price by Rs. 50 changes the situation from a 10% loss to a 5% profit. This yields an equation linking x and 50. Once x is found, we compute the loss and profit amounts and then find their ratio as a percentage. Step-by-Step Solution: Let the cost price of the smartphone be x rupees. At 10% loss, selling price SP1 = 0.90x. If sold for Rs. 50 more, new selling price SP2 = SP1 + 50 = 0.90x + 50. This new selling price corresponds to 5% profit, so SP2 = 1.05x. Equate the two expressions for SP2: 0.90x + 50 = 1.05x. Rearrange: 50 = 1.05x − 0.90x = 0.15x. Therefore, x = 50 / 0.15 = 333.33 (approximate). Loss amount at SP1 = 10% of x = 0.10x. Profit amount at SP2 = 5% of x = 0.05x. Now compute the ratio: loss / profit = 0.10x / 0.05x = 2. Expressed as a percentage: 2 * 100% = 200%. Verification / Alternative check: Take x = Rs. 333.33 approximately. Then SP1 at 10% loss is 0.90 * 333.33 ≈ Rs. 300. SP2 at 5% profit is 1.05 * 333.33 ≈ Rs. 350. The difference between SP2 and SP1 is about Rs. 50, which matches the given information. Loss amount is about Rs. 33.33 and profit amount is about Rs. 16.67. The ratio 33.33 / 16.67 is approximately 2, or 200%. Why Other Options Are Wrong: 100%: This would mean the loss equals the profit, which contradicts our ratio of 2:1. 75% and 85%: These suggest the loss is smaller than the profit, which does not fit the algebraic relationship derived from the given prices. 150%: This is closer but still not equal to the exact ratio of 2:1 (200%). Common Pitfalls: Learners may confuse loss percentage and profit percentage and think that the difference of 15% directly gives the ratio. Another common error is to forget that the Rs. 50 difference is between two selling prices, not between cost price and selling price. Always explicitly express both selling prices in terms of cost price, equate them using the problem condition and then compare the actual loss and profit amounts. Final Answer: The initial loss is 200% of the profit that would have been earned at 5% profit.

Question 18

Raghu buys an article for Rs. 14,360 and spends an additional Rs. 240 on its transportation. At what selling price should he sell the article in order to earn a profit of 15% on his total cost (including transportation)?

Accepted Answer

Introduction / Context: This question tests the calculation of selling price when there are additional expenses over and above the purchase price. Raghu buys an article and also incurs transportation charges. His profit percentage must be calculated on the total cost, which includes both the purchase cost and the transportation cost. Such questions are common in profit and loss topics, particularly to check whether candidates correctly include all cost components in the cost price. Given Data / Assumptions: Purchase price of the article = Rs. 14,360. Transportation cost = Rs. 240. Desired profit percentage on total cost = 15%. We must find the required selling price (SP) to achieve this profit. Concept / Approach: The effective cost price includes all expenses incurred to make the article ready for sale. Thus, total cost price = purchase price + transportation charges. Once we know the total cost price, we apply the profit formula: SP = CP * (1 + profit%). For a 15% profit, we multiply the total cost by 1.15 to get the required selling price. Step-by-Step Solution: Purchase price of the article = Rs. 14,360. Transportation charges = Rs. 240. Total cost price (CP) = 14,360 + 240. CP = Rs. 14,600. Desired profit percentage = 15%. Selling price SP = CP * (1 + profit percentage / 100). So SP = 14,600 * (1 + 15 / 100) = 14,600 * 1.15. Compute 14,600 * 1.15 = 14,600 + 0.15 * 14,600. 0.15 * 14,600 = 2,190. Therefore, SP = 14,600 + 2,190 = Rs. 16,790. Verification / Alternative check: We can verify by computing the actual profit. Profit = SP − CP = 16,790 − 14,600 = Rs. 2,190. Profit percentage = (2,190 / 14,600) * 100. Now 2,190 / 14,600 = 0.15, giving 0.15 * 100 = 15%. This matches the desired profit percentage, confirming that Rs. 16,790 is correct. Why Other Options Are Wrong: 16,000: The profit here would be only 1,400, which is less than 10% of the cost price. 16,150: This gives a profit of 1,550, which is close but still below 15% when you compute the percentage accurately. 16,500: This corresponds to a profit of 1,900, which is approximately 13% and not 15%. 15,900: This is even closer to the cost price and yields a profit under 10%, far from the required profit rate. Common Pitfalls: A very common mistake is to ignore the transportation cost and calculate profit only on the purchase price. Another error is to miscalculate the percentage increase by adding 15 directly to the cost instead of multiplying by 1.15. To avoid these issues, always combine all cost components first and then apply the profit percentage formula accurately. Final Answer: Raghu should sell the article for Rs. 16,790 to earn a 15% profit on his total cost.

Question 19

The marked price of an article is Rs. 1,600 more than its cost price. When the article is sold at a discount of Rs. 500 on the marked price, the shopkeeper earns a profit of 25% on the cost price. For the shopkeeper to earn a profit of 30% on the sa…

Accepted Answer

Introduction / Context: This problem combines the ideas of marked price, discount and profit percentage. The marked price of an article is set higher than its cost price by a fixed amount. When a discount is given, the selling price changes and so does the profit. We are told that a certain discount results in a 25% profit and then asked to find a new selling price that would produce a 30% profit on the same cost price. This is a typical profit and loss question that tests algebraic manipulation of prices and percentages. Given Data / Assumptions: Let the cost price (CP) of the article be C. The marked price (MP) is C + Rs. 1,600. When a discount of Rs. 500 is allowed on MP, the resulting selling price gives a 25% profit. We must find the selling price that would yield a 30% profit on the same cost price C. Concept / Approach: We use two main profit relationships. First, with the discount of Rs. 500, the selling price is MP − 500, which equals C plus 25% of C. From this, we can solve for C. Once C is known, the required selling price for a 30% profit is simply C * 1.30. The trick is to correctly interpret the relationship between marked price, discount and profit, and express everything in terms of C. Step-by-Step Solution: Let cost price = C rupees. Marked price MP = C + 1,600. When a discount of Rs. 500 is given, selling price SP1 = MP − 500 = C + 1,600 − 500. Thus, SP1 = C + 1,100. We are told this selling price yields a 25% profit on C. So SP1 = C * 1.25. Therefore, C + 1,100 = 1.25C. Rearrange: 1.25C − C = 1,100. 0.25C = 1,100. C = 1,100 / 0.25 = 4,400 rupees. Now, to earn a 30% profit, required selling price SP2 = 1.30C = 1.30 * 4,400. SP2 = 4,400 * 1.30 = 5,720 rupees. Verification / Alternative check: Check the first scenario. With C = 4,400, MP = 4,400 + 1,600 = 6,000. Discount of Rs. 500 means SP1 = 6,000 − 500 = 5,500. Profit = 5,500 − 4,400 = 1,100. Profit percentage = (1,100 / 4,400) * 100 = 25%, which matches the given condition. For SP2, we tested 5,720, and profit = 5,720 − 4,400 = 1,320. Profit percentage = (1,320 / 4,400) * 100 = 30%, confirming correctness. Why Other Options Are Wrong: 5,740 and 5,730: These yield profit percentages slightly above or below 30% when compared with 4,400. 5,620: This gives profit = 1,220, so profit percentage is (1,220 / 4,400) * 100 ≈ 27.73%, not 30%. 5,800: Corresponds to a higher profit percentage, greater than 30% and not consistent with the question. Common Pitfalls: One frequent mistake is to calculate the 25% profit on the marked price instead of the cost price. Another is to add or subtract profit percentages directly to or from the discount amount. The correct method is always to express selling price in terms of cost price and then apply the given conditions step by step. Also, note that the 1,600 rupees difference is between MP and CP, not between SP and CP. Final Answer: To earn a 30% profit on the cost price, the article should be sold for Rs. 5,720.

Question 20

A dishonest shopkeeper claims to sell grocery items at cost price but actually uses a false weight of 900 grams while charging customers for 1 kilogram. Assuming his listed cost price is for 1,000 grams, what is his percentage gain due to using the …

Accepted Answer

Introduction / Context: This question involves cheating by using a false weight while claiming to sell at cost price. The shopkeeper pretends to give 1 kilogram but actually delivers only 900 grams. Since customers pay for 1 kilogram but receive less, the shopkeeper earns an effective profit without changing the labelled price. Calculating this gain requires understanding that the cost is for the actual quantity supplied, whereas the revenue is based on the claimed quantity. Given Data / Assumptions: The cost price (CP) is quoted for 1,000 grams (1 kilogram) of grocery. The shopkeeper uses a false weight of 900 grams but charges customers for 1 kilogram. He sells at the listed cost price per kilogram, so there is no apparent price markup. Water or any other adulteration is not mentioned; only weight cheating is considered. We must find his percentage gain based purely on short-weighting. Concept / Approach: The trick is to assume a convenient cost price for 1 kilogram and then consider how much the shopkeeper pays for 900 grams. Since the selling price is equal to the cost price of 1,000 grams, but he only delivers 900 grams, the difference between revenue and actual cost of 900 grams is the profit. Profit percentage is then calculated as usual: profit% = (profit / cost price of quantity sold) * 100. Step-by-Step Solution: Assume cost price of 1 kg of grocery = Rs. 1 (for easy calculation). Therefore, cost price per gram = Rs. 1 / 1,000. Actual quantity given to customer = 900 grams. Cost of 900 grams = 900 * (1 / 1,000) = Rs. 0.90. The shopkeeper charges the customer for 1 kg at cost price, so selling price (SP) = Rs. 1. Profit = SP − CP (for 900 g) = 1 − 0.90 = Rs. 0.10. Profit percentage = (Profit / Cost price of quantity sold) * 100. Profit percentage = (0.10 / 0.90) * 100. 0.10 / 0.90 = 1 / 9 ≈ 0.1111. Therefore, profit percentage ≈ 0.1111 * 100 = 11.11% = 100/9%. Verification / Alternative check: We can also assume any other cost price, for example Rs. 90 for 1 kg. Then CP for 900 grams = 0.9 * 90 = Rs. 81. He charges the customer Rs. 90 for this quantity. Profit = 90 − 81 = Rs. 9. Profit percentage = (9 / 81) * 100 = (1 / 9) * 100 = 11.11%, again confirming 100/9% as the exact fractional form. Why Other Options Are Wrong: 91/9% and 95/9%: These correspond to much larger profit percentages and arise from misinterpreting the cost base or using the wrong reference quantity. 100/11%: This is a different fraction and does not match the computed ratio of 1/9. 11.11%: While numerically equivalent to 100/9%, the answer options are expected in fractional form, and 100/9% is the more precise representation given in the choices. Common Pitfalls: Some students incorrectly treat the cost price as that of 900 grams instead of 1,000 grams, or they apply profit percentage on selling price instead of cost price. Another common mistake is forgetting to convert grams to kilograms consistently or using 100 grams as a base instead of 1,000 grams, which can change the numbers. Always choose a simple assumption (like CP = Rs. 1 for 1 kg) and then compute the cost of the actual quantity delivered. Final Answer: The dishonest shopkeeper's gain due to using a false 900 gram weight is 100/9%, which is approximately 11.11%.

Profit and Loss Questions