Question 1

The cost price of a calculator is Rs 495. If the profit percentage on selling it is 40%, what is the profit amount in rupees?

Accepted Answer

Introduction / Context: This is a simple direct application of profit percentage. Once cost price and profit percent are known, the actual profit amount can be obtained easily. Such questions appear frequently to check whether you know and can quickly apply the basic percentage formula involving cost price and profit. Given Data / Assumptions: Cost price (CP) of the calculator is Rs 495. Profit percentage on selling is 40%. We are asked to find the profit amount in rupees, not the selling price. Concept / Approach: The formula for profit amount when cost price and profit percent are known is: Profit = CP * profit_percent / 100. Selling price is then CP + Profit if required. In this question we only need the profit amount, so a single multiplication is enough. Step-by-Step Solution: Cost price CP = Rs 495.Profit percentage = 40%.Profit amount = CP * profit_percent / 100.Profit = 495 * 40 / 100.Profit = 495 * 0.40 = Rs 198.Therefore the shopkeeper earns a profit of Rs 198 on the calculator. Verification / Alternative check: If we want to verify, we can find the selling price as well. Selling price SP = CP + Profit = 495 + 198 = Rs 693. Now profit percentage = (SP - CP) / CP * 100 = (693 - 495) / 495 * 100 = 198 / 495 * 100 = 40%, which matches the given profit percentage and confirms that the profit amount of Rs 198 is correct. Why Other Options Are Wrong: Values like Rs 186, Rs 218 or Rs 226, when added to 495, would give selling prices that correspond to profit percentages different from 40%. For example, 186 / 495 * 100 is less than 40%, and 226 / 495 * 100 is more than 40%. Only Rs 198 yields exactly 40% profit on Rs 495. Common Pitfalls: Students sometimes confuse profit percentage with the percentage of the selling price instead of the cost price. Others might mistakenly compute 495 * 0.04 or make arithmetic errors in multiplication. Writing the formula clearly and handling the decimal multiplication carefully reduces the chance of mistakes. Final Answer: The profit earned on the calculator is Rs 198.

Question 2

A shopkeeper sells 9 Rolex watches and earns a total profit equal to the selling price of 4 Rolex watches. What is his profit percentage on each watch?

Accepted Answer

Introduction / Context: This question examines the link between total profit on multiple items and profit percentage on each item when all are sold at the same price. Instead of giving the cost or selling prices directly, it describes profit in terms of the selling price of some of the items. This type of question is common in aptitude exams because it tests your ability to set up equations based on a word description. Given Data / Assumptions: 9 Rolex watches are sold. Total profit earned is equal to the selling price of 4 Rolex watches. All watches are identical and sold at the same selling price. We need to find the profit percentage on each watch. Concept / Approach: Let cost price per watch be C and selling price per watch be S. Total cost for 9 watches is 9C, and total selling price is 9S. The total profit is 9S - 9C. The question states that this total profit equals the selling price of 4 watches, that is 4S. This gives an equation involving S and C. Once we determine S in terms of C, we can compute profit percentage as (S - C) / C * 100. Step-by-Step Solution: Let cost price of one watch be C and selling price of one watch be S.Total profit on 9 watches = 9S - 9C.Given this profit equals the selling price of 4 watches, so 9S - 9C = 4S.Rearrange: 9S - 4S = 9C, so 5S = 9C.Therefore S = 9C / 5 = 1.8C.Profit per watch = S - C = 1.8C - C = 0.8C.Profit percentage = (0.8C / C) * 100 = 80%. Verification / Alternative check: Take an easy value, for example C = Rs 100. Then S = 1.8 * 100 = Rs 180. Total cost for 9 watches = 9 * 100 = Rs 900. Total selling price = 9 * 180 = Rs 1620. Profit = 1620 - 900 = Rs 720. Selling price of 4 watches = 4 * 180 = Rs 720, which matches the given condition, confirming our calculations. Profit percentage per watch is (180 - 100) / 100 * 100 = 80% as derived. Why Other Options Are Wrong: 44.4 percent, 88.8 percent or 8.8 percent are not compatible with the relationship 9S - 9C = 4S. Using any of those values leads to different equations between S and C and fails to reproduce the given profit description. Only 80 percent satisfies the exact condition described in the problem. Common Pitfalls: Some learners divide 4 by 9 and directly treat it as the profit percentage, which is incorrect. Others may confuse the total profit with profit per watch and set up an incorrect equation. Carefully defining variables and writing a clear total profit equation helps avoid such mistakes. Final Answer: The profit percentage on each Rolex watch is 80 percent.

Question 3

A wholesaler sells a watch to a retailer at a gain of 37%, and the retailer sells it to a customer at a loss of 25%. If the customer pays Rs 2620.125, what was the original cost price of the watch for the wholesaler?

Accepted Answer

Introduction / Context: This question extends the idea of successive percentage changes in a trade chain where first a wholesaler gains, and then a retailer incurs a loss. Despite opposite directions, both percentage changes are multiplicative. The final price given is the sale price to the customer, and we must work backwards to find what the wholesaler originally paid for the watch. Given Data / Assumptions: The wholesaler sells to the retailer at a gain of 37%. The retailer sells to the customer at a loss of 25% on his purchase price. The customer pays Rs 2620.125 for the watch. We assume there are no additional discounts, taxes or costs. Concept / Approach: Let the wholesaler cost price be CPw. When he sells to the retailer at 37% gain, the retailer buying price is CPw * 1.37. The retailer then sells at a loss of 25%, so selling price to the customer is (CPw * 1.37) * 0.75. This combined multiplier is 1.37 * 0.75 = 1.0275. Given the final price, we can divide by 1.0275 to find CPw. Step-by-Step Solution: Let CPw be the cost price of the watch for the wholesaler.Price to retailer = CPw * (1 + 37 / 100) = CPw * 1.37.Retailer sells at 25% loss, so selling price to customer SP = (CPw * 1.37) * (1 - 25 / 100) = CPw * 1.37 * 0.75.Thus SP = CPw * 1.0275.Given SP = Rs 2620.125.So CPw * 1.0275 = 2620.125.CPw = 2620.125 / 1.0275 = Rs 2550. Verification / Alternative check: Starting with CPw = Rs 2550, price to retailer at 37% gain is 2550 * 1.37 = Rs 3493.5. Retailer then sells at 25% loss: SP = 3493.5 * 0.75 = Rs 2620.125, which exactly matches the given customer price. This confirms that the wholesaler cost price of Rs 2550 is correct. Why Other Options Are Wrong: Numbers like Rs 2692, Rs 3327 or Rs 2408, when multiplied by 1.0275, do not yield Rs 2620.125. They would produce higher or lower final prices, so they do not satisfy the given chain of profit and loss. Only Rs 2550 reproduces the exact selling price to the customer after both percentage changes. Common Pitfalls: Some candidates incorrectly subtract or add percentages directly instead of using multiplicative factors, or they may confuse the base for loss (retailer cost price) with the base for gain (wholesaler cost). Another frequent mistake is rounding off early, which can disturb the final answer when decimals are involved. Keeping all steps algebraic until the end helps maintain accuracy. Final Answer: The original cost price of the watch for the wholesaler was Rs 2550.

Question 4

When a discount of 20% is given on a jacket, the profit is 28%. If instead the discount is reduced to 13% on the same marked price, what will be the profit percentage?

Accepted Answer

Introduction / Context: This question is very similar to earlier discount and profit problems. It explores how changing the discount on a fixed marked price alters the final profit percentage, given that cost price remains constant. Such questions are standard when learning how selling strategies affect margins in retail scenarios. Given Data / Assumptions: At 20% discount, the seller gets 28% profit. At 13% discount, we need to find the new profit percentage. The marked price of the jacket is constant in both cases. The cost price remains unchanged. Concept / Approach: Let CP be cost price and MP be marked price. With a 20% discount, SP1 = MP * 0.80 = CP * 1.28. This equality lets us express MP in terms of CP. Then, with a 13% discount, SP2 = MP * 0.87. Substituting MP from the first relation, we find SP2 in terms of CP and compute profit percentage as (SP2 - CP) / CP * 100. Step-by-Step Solution: Let CP be the cost price and MP the marked price of the jacket.With 20% discount, SP1 = MP * (1 - 20 / 100) = 0.80 * MP.Profit here is 28%, so SP1 = CP * 1.28.Thus 0.80 * MP = 1.28 * CP, so MP = (1.28 / 0.80) * CP = 1.6 * CP.With 13% discount, SP2 = MP * (1 - 13 / 100) = 0.87 * MP.Substituting MP, SP2 = 0.87 * 1.6 * CP = 1.392 * CP.Profit percentage now = (SP2 - CP) / CP * 100 = (1.392 * CP - CP) / CP * 100 = 0.392 * 100 = 39.2 percent. Verification / Alternative check: Assume CP = Rs 100. Then MP = 1.6 * 100 = Rs 160. With 20% discount, SP1 = 0.80 * 160 = Rs 128, which is exactly 28% profit on Rs 100. With 13% discount, SP2 = 0.87 * 160 = Rs 139.2. Profit = 39.2 on cost 100, i.e., 39.2%. This confirms that our result is consistent. Why Other Options Are Wrong: 41 percent, 42.8 percent or 37.4 percent all correspond to different selling prices for the same cost price and do not match the actual SP2 derived from the discount formula. Only 39.2 percent exactly matches the change from 20% discount with 28% profit to 13% discount. Common Pitfalls: Students may try to simply add 7 percentage points to the profit when the discount is reduced by 7 percentage points, which is not generally valid because discounts work on marked price and profits on cost price. Another common error is to miscalculate the multiplier for profit and discount combinations. Writing each step clearly in terms of CP and MP helps avoid such mistakes. Final Answer: With a 13% discount, the profit on the jacket is 39.2 percent.

Question 5

The marked price of a helmet is 30% more than its cost price. If the helmet is sold for Rs 744 after allowing a discount of Rs 36 on the marked price, what is the profit percentage?

Accepted Answer

Introduction / Context: This question ties together the relation between cost price, marked price, discount and profit. The marked price is given in relation to cost price, and the final selling price is given after a flat discount. From this, we must backtrack to find the cost price and then compute the profit percentage. This reflects real shop scenarios where products are marked up and then discounted to attract customers while preserving profit. Given Data / Assumptions: Marked price is 30% above cost price. Discount given on the marked price is Rs 36. Final selling price after discount is Rs 744. We need to find the profit percentage. Concept / Approach: Let cost price be CP and marked price be MP. We are told MP = CP * 1.30. The selling price is MP minus a fixed discount of Rs 36, and this equals Rs 744. From that, MP can be obtained as 744 + 36. Once MP is known, we find CP using MP = 1.30 * CP. With CP and final SP known, profit percentage formula (SP - CP) / CP * 100 gives the answer. Step-by-Step Solution: Let CP be the cost price and MP the marked price of the helmet.MP is 30% above CP, so MP = 1.30 * CP.The helmet is sold for Rs 744 after a discount of Rs 36 on MP.Therefore selling price SP = MP - 36 = Rs 744, so MP = 744 + 36 = Rs 780.Now 780 = 1.30 * CP, so CP = 780 / 1.30 = Rs 600.Profit amount = SP - CP = 744 - 600 = Rs 144.Profit percentage = (144 / 600) * 100 = 24%. Verification / Alternative check: We can verify by reversing the steps. Take CP = Rs 600. Marked price at 30% above CP is 600 * 1.30 = Rs 780. Apply a flat discount of Rs 36 to get SP = 780 - 36 = Rs 744. Compare SP with CP: profit is Rs 144 on Rs 600, which is 24%. Everything is consistent with the given conditions. Why Other Options Are Wrong: A profit of 18%, 21% or 27% would require different relationships between CP, MP and SP. For example, 18% profit would give SP = 600 * 1.18 = Rs 708, not Rs 744. Hence these options do not match the numerical connection among cost, margin and discount described in the question. Only 24% is correct. Common Pitfalls: Some students mistakenly discount from cost price instead of marked price, which changes the arithmetic completely. Others may misinterpret 30% above cost price as 30% of the final selling price. Keeping track of which value each percentage relates to (CP or MP) is crucial to solving such problems correctly. Final Answer: The profit percentage on selling the helmet is 24%.

Question 6

A dealer sold an article at a loss of 6%. Had he sold it for Rs 64 more, he would have made a profit of 10%. What was the cost price of the article?

Accepted Answer

Introduction / Context: This question tests your ability to connect two different selling situations for the same article, one with a loss and one with a profit, and to use the difference in selling price to deduce the cost price. It is a standard type of profit and loss problem where two percentage conditions are given along with an absolute difference in rupees. Given Data / Assumptions: The article is first sold at a loss of 6%. If it had been sold for Rs 64 more, there would have been a profit of 10%. We need to find the cost price of the article. Cost price is the same in both hypothetical selling situations. Concept / Approach: Let cost price be CP. Selling price at 6% loss is CP * (1 - 6 / 100) = 0.94 * CP. Selling price at 10% profit is CP * (1 + 10 / 100) = 1.10 * CP. The difference between these two selling prices is given as Rs 64. So we set 1.10 * CP - 0.94 * CP = 64 and solve for CP. Step-by-Step Solution: Let CP be the cost price of the article.SP1 at 6% loss = 0.94 * CP.SP2 at 10% profit = 1.10 * CP.Given SP2 is Rs 64 more than SP1, so SP2 - SP1 = 64.Therefore 1.10 * CP - 0.94 * CP = 64.0.16 * CP = 64.CP = 64 / 0.16 = 400.So the cost price of the article is Rs 400. Verification / Alternative check: Take CP = Rs 400. At 6% loss, SP1 = 400 * 0.94 = Rs 376. At 10% profit, SP2 = 400 * 1.10 = Rs 440. The difference SP2 - SP1 = 440 - 376 = Rs 64, which exactly matches the condition in the question. This confirms that the cost price of Rs 400 is correct. Why Other Options Are Wrong: If CP were Rs 200, the difference between 10% profit price and 6% loss price would be 0.16 * 200 = Rs 32, not Rs 64. Similarly, CP of Rs 164 or Rs 464 would also yield incorrect differences. Only CP = Rs 400 results in a difference of Rs 64 between the two selling scenarios. Common Pitfalls: One common mistake is to forget that both percentages are applied to the same cost price and instead try to use the difference between 10% and 6% directly on some selling price. Another error is in simple arithmetic with decimals and percentages. Carefully writing the equations with multipliers makes the structure clear and avoids confusion. Final Answer: The cost price of the article is Rs 400.

Question 7

If the ratio of cost price to selling price of an article is 10 : 11, what is the profit percentage made on selling the article?

Accepted Answer

Introduction / Context: This is a direct ratio based profit question. Instead of giving the actual cost and selling prices, the question provides their ratio. From this, you must determine the profit percentage. Such ratio forms are common in aptitude tests because they simplify arithmetic while still checking your understanding of how profit percent is defined. Given Data / Assumptions: Ratio of cost price (CP) to selling price (SP) is 10 : 11. We need to find the profit percentage. There are no extra costs or discounts involved. Concept / Approach: If CP : SP = 10 : 11, we can assume CP = 10 units and SP = 11 units. Profit is SP - CP in the same units. Profit percent is then (Profit / CP) * 100. This approach of working with proportional units instead of actual rupees is a standard shortcut in ratio problems. Step-by-Step Solution: Given CP : SP = 10 : 11.Assume CP = 10 units and SP = 11 units.Profit = SP - CP = 11 - 10 = 1 unit.Profit percentage = (Profit / CP) * 100.Profit percentage = (1 / 10) * 100 = 10%.Therefore the profit made is 10%. Verification / Alternative check: Take a concrete example: let CP be Rs 100. From the ratio 10 : 11, SP must be Rs 110. Profit is Rs 10 on a cost of Rs 100, so percentage profit = 10 / 100 * 100 = 10%. This matches our earlier unit based calculation and confirms the result. Why Other Options Are Wrong: 1% profit would arise if SP were 10.1 for CP 10, 5% if SP were 10.5, and 8% if SP were 10.8 given CP of 10. None of these matches the ratio 10 : 11. Only 10% profit matches the CU ratio of 10 : 11 for cost and selling prices. Common Pitfalls: Students sometimes invert the ratio and treat it as SP : CP instead of CP : SP, which would lead to a completely different answer. Carefully reading the statement and assigning the ratio correctly is very important. Another mistake is to confuse profit percentage with the ratio of SP to CP directly without subtracting CP from SP first. Final Answer: The profit percentage on the article is 10%.

Question 8

A trader buys 500 kg of cotton for Rs 9000. Due to rain, 10% of the cotton is spoiled and becomes unsaleable. At what rate per kg should he sell the remaining cotton in order to earn an overall profit of 10%?

Accepted Answer

Introduction / Context: This question combines loss of quantity due to spoilage with the requirement of a target profit on the original investment. It shows a realistic business situation in which not all purchased goods can be sold. You must adjust the selling price of the remaining good quality cotton so that, despite the loss of some stock, the trader still earns a desired profit percentage overall. Given Data / Assumptions: Total quantity of cotton bought = 500 kg. Total cost = Rs 9000. 10% of the cotton is spoiled and cannot be sold. The trader wants an overall profit of 10% on his investment. We assume spoiled cotton has no resale value. Concept / Approach: First, we find how many kilograms of cotton remain saleable after spoilage. Then we calculate the total revenue required to get a 10% profit on the total cost. Finally, the required selling price per kg is that revenue divided by the saleable quantity. This is a standard approach: Desired Revenue = Cost * (1 + profit_percent / 100). Step-by-Step Solution: Total quantity purchased = 500 kg.Total cost price = Rs 9000.Spoiled cotton = 10% of 500 kg = 0.10 * 500 = 50 kg.Saleable cotton = 500 kg - 50 kg = 450 kg.Trader wants 10% profit, so required total revenue = 9000 * (1 + 10 / 100) = 9000 * 1.10 = Rs 9900.Required selling price per kg = 9900 / 450.9900 / 450 = Rs 22 per kg. Verification / Alternative check: If he sells 450 kg at Rs 22 per kg, revenue = 450 * 22 = Rs 9900. Initial cost was Rs 9000, so profit = 9900 - 9000 = Rs 900. Profit percentage = 900 / 9000 * 100 = 10%. This confirms that selling at Rs 22 per kg achieves the desired overall gain despite 10% spoilage. Why Other Options Are Wrong: If he sells at Rs 20 per kg, revenue is 450 * 20 = Rs 9000, which gives no profit. At Rs 25 or Rs 30 per kg, profits would be much higher than 10%. For instance, at Rs 25, revenue is Rs 11250, giving 25% profit. Thus only Rs 22 per kg gives exactly a 10% profit on the total investment. Common Pitfalls: Some learners mistakenly try to apply the profit percentage only to the uns spoiled quantity or misinterpret the base for the profit calculation. Profit is always calculated on the original cost, not on the value of the remaining quantity. Another error is forgetting that the spoiled portion contributes zero revenue, which must be considered implicitly in the rate adjustment for the uns spoiled portion. Final Answer: The trader should sell the remaining cotton at Rs 22 per kg to earn a 10% profit.

Question 9

A vendor buys bananas at the rate of 9 for Rs 8 and sells them at the rate of 8 for Rs 9. What is his profit or loss percentage?

Accepted Answer

Introduction / Context: This is another unit rate profit and loss question, similar to the oranges problem. Instead of giving direct per unit prices, the vendor's buying and selling prices are described in terms of groups of bananas. The task is to compute cost price per banana and selling price per banana and then determine the percentage profit or loss. Given Data / Assumptions: The vendor buys 9 bananas for Rs 8. He sells 8 bananas for Rs 9. We must find the profit or loss percentage. All bananas bought are sold and there is no wastage. Concept / Approach: First we find cost per banana: CP per banana = total cost divided by number of bananas purchased. Then we find selling price per banana: SP per banana = total selling price divided by number of bananas sold. Using these, we compute Profit% = (SP - CP) / CP * 100. Since one group relates 9 bananas to Rs 8 and the other relates 8 bananas to Rs 9, converting to per piece rates is essential. Step-by-Step Solution: Buying rate: 9 bananas cost Rs 8, so CP per banana = 8 / 9 rupees.Selling rate: 8 bananas sell for Rs 9, so SP per banana = 9 / 8 rupees.CP per banana = 8 / 9 ≈ 0.8889.SP per banana = 9 / 8 = 1.125.Profit per banana = SP - CP = 1.125 - 0.8889 ≈ 0.2361.Profit percentage = (profit per banana / CP per banana) * 100 ≈ (0.2361 / 0.8889) * 100.0.2361 / 0.8889 ≈ 0.265625, so profit percentage ≈ 26.5625%.Rounded suitably, this is 26.56% profit. Verification / Alternative check: Take a common multiple of the quantities to avoid decimals. For example, buy 72 bananas. At 9 for Rs 8, number of groups is 72 / 9 = 8, so cost = 8 * 8 = Rs 64. Sell 72 bananas at 8 for Rs 9, groups = 72 / 8 = 9, total revenue = 9 * 9 = Rs 81. Profit = 81 - 64 = Rs 17. Profit percentage = 17 / 64 * 100 ≈ 26.5625%, confirming the earlier calculation. Why Other Options Are Wrong: 13.28% profit or loss values correspond to roughly half the correct percentage and result from miscalculations or using inverse ratios. 26.56% loss is impossible here because SP per banana is larger than CP per banana. Only 26.56% profit matches the numbers derived from consistent per unit comparisons. Common Pitfalls: Some learners invert one of the fraction rates or compare 9 for 8 and 8 for 9 directly without converting to per banana figures. This can lead to wrong conclusions about whether there is profit or loss. Always reduce such grouped rate problems to per unit prices and then apply the profit formula systematically. Final Answer: The vendor makes a 26.56% profit on selling the bananas.

Question 10

If the selling price of an item is tripled and its cost price is doubled, the profit becomes 65%. What is the present profit percentage on the item?

Accepted Answer

Introduction / Context: This question describes a hypothetical change in both selling price and cost price and tells us the resulting profit percentage. From that altered situation, we need to deduce what the original profit percentage was. It checks your ability to form algebraic equations with unknown cost and selling prices and to interpret percentages correctly. Given Data / Assumptions: Original cost price is C and original selling price is S. New cost price is doubled, that is 2C. New selling price is tripled, that is 3S. Under these new conditions, profit percentage becomes 65%. We have to find the original profit percentage based on original C and S. Concept / Approach: Profit percentage is defined as Profit / Cost * 100. For the new scenario, profit is 3S - 2C and cost is 2C. Given profit percentage is 65%, so (3S - 2C) / (2C) * 100 = 65. This gives an equation relating S and C. Solving for S in terms of C allows us to calculate original profit percentage, which is (S - C) / C * 100. Step-by-Step Solution: Let original cost price be C and original selling price be S.In the modified case, cost price = 2C and selling price = 3S.Profit in modified case = 3S - 2C.Given profit percentage in modified case = 65%, so (3S - 2C) / (2C) * 100 = 65.Thus (3S - 2C) / (2C) = 0.65.3S - 2C = 0.65 * 2C = 1.3C.3S = 2C + 1.3C = 3.3C, so S = 3.3C / 3 = 1.1C.Original profit = S - C = 1.1C - C = 0.1C.Original profit percentage = (0.1C / C) * 100 = 10%. Verification / Alternative check: To verify numerically, assume C = Rs 100. Then S = 1.1 * 100 = Rs 110. Original profit percentage is (110 - 100) / 100 * 100 = 10%. In the modified scenario, cost becomes 2 * 100 = Rs 200 and selling price becomes 3 * 110 = Rs 330. Profit = 330 - 200 = Rs 130. Profit percentage = 130 / 200 * 100 = 65%, which matches the given condition and confirms that the original profit percentage is 10%. Why Other Options Are Wrong: Profit percentages like 15%, 20% or 25% correspond to different relationships between S and C, leading to different values of 3S - 2C in the modified scenario. For these values, the profit percentage in the modified case would not be 65%. Only a 10% original profit is consistent with the equation derived from the given information. Common Pitfalls: Some students incorrectly treat the change as 3S - 2C equal to 65 directly or forget to divide by 2C when setting up the percentage equation. Another error is mixing up which quantity is doubled and which is tripled. Carefully aligning the profit formula with the modified values avoids these mistakes. Final Answer: The present profit percentage on the item is 10%.

Question 11

A vendor sells a coconut for Rs 24 and suffers a loss of 24%. If he wants to make a profit of 14% on the cost price instead, at what price (in rupees) should he sell the coconut?

Accepted Answer

Introduction / Context: This question is another example of moving from a known loss situation to a required profit situation on the same item. By using the loss information, we deduce the cost price and then use that cost price to find the selling price that would give a desired profit percentage. It is a direct application of profit and loss formulas. Given Data / Assumptions: The coconut is sold for Rs 24 at a loss of 24%. The vendor wants instead to gain 14% on the cost price. We must find the new selling price to achieve this 14% profit. The cost price is the same in both cases. Concept / Approach: When there is a loss of 24%, the selling price equals 76% of the cost price because 100% - 24% = 76%. Thus SP1 = 0.76 * CP. From the given SP1, we can find CP by dividing by 0.76. Then, to get a 14% profit, the new selling price SP2 must be CP * 1.14. This two step process, first to recover CP and then to apply a new profit percentage, is standard. Step-by-Step Solution: Let CP be the cost price of the coconut.Given loss = 24%, so SP1 = CP * (1 - 24 / 100) = 0.76 * CP.We are told SP1 = Rs 24.So 0.76 * CP = 24, hence CP = 24 / 0.76.CP = 24 / 0.76 ≈ Rs 31.5789.For a profit of 14%, SP2 = CP * (1 + 14 / 100) = 1.14 * CP.SP2 ≈ 1.14 * 31.5789 ≈ Rs 36.Thus the vendor should sell the coconut for Rs 36 to earn a 14% profit. Verification / Alternative check: Using an exact fraction approach, 24% loss means SP1 = 76% of CP, so CP = 24 * 100 / 76 = 2400 / 76 = 600 / 19 = about 31.5789. Then SP2 = CP * 114 / 100 = (600 / 19) * 114 / 100 = (600 * 114) / (19 * 100) = 68400 / 1900 = 36 exactly. So there is no rounding error and the exact required selling price is Rs 36. Why Other Options Are Wrong: At Rs 28 or Rs 30 or Rs 32, the profit percentage on a cost price of about Rs 31.58 would be far less than 14%, with Rs 28 and Rs 30 still giving losses and Rs 32 giving only a small profit. Only Rs 36 gives exactly 14% profit on the computed cost price. Common Pitfalls: Some learners mistakenly compute the new price by simply adding 38 percentage points to the old selling price or by using 24% and 14% directly on Rs 24, which is incorrect. Profit and loss percentages must be applied on cost price, not on previous selling prices. It is essential to recover the cost price first and then apply the new desired profit percentage. Final Answer: The vendor should sell the coconut for Rs 36 to earn a 14% profit.

Question 12

A villager buys a goat and a sheep together for Rs 14250. He sells the sheep at a profit of 10% and the goat at a loss of 20%, but sells both animals at the same selling price. What was the cost price of the cheaper animal?

Accepted Answer

Introduction / Context: This problem involves two different animals bought together and sold under different profit and loss conditions, but at the same final selling price. Such a setup leads to a pair of equations in terms of cost prices. This question helps you practice forming and solving linear equations from worded profit and loss conditions, which is a common theme in aptitude tests. Given Data / Assumptions: Total cost price of goat and sheep together is Rs 14250. The sheep is sold at 10% profit. The goat is sold at 20% loss. Both animals are sold at the same selling price. We need the cost price of the cheaper animal. Concept / Approach: Let the cost price of the goat be G and that of the sheep be S. Then G + S = 14250. Sheep is sold at 10% profit, so its selling price is 1.10 * S. Goat is sold at 20% loss, so its selling price is 0.80 * G. These selling prices are equal. From this equality and the total cost equation, we can solve for G and S. The smaller of the two is the cheaper animal's cost price. Step-by-Step Solution: Let cost price of goat = G and cost price of sheep = S.Total cost price: G + S = 14250. (Equation 1)Sheep is sold at 10% profit, so selling price of sheep = 1.10 * S.Goat is sold at 20% loss, so selling price of goat = 0.80 * G.Given both are sold at the same price, so 1.10 * S = 0.80 * G. (Equation 2)From Equation 2, G = (1.10 / 0.80) * S = (11 / 8) * S = 1.375 * S.Substitute in Equation 1: 1.375 * S + S = 14250.2.375 * S = 14250.S = 14250 / 2.375 = 6000.Therefore G = 14250 - 6000 = 8250.The cheaper animal is the sheep, costing Rs 6000. Verification / Alternative check: Check selling prices. Sheep CP = Rs 6000, sold at 10% profit, so SPsheep = 6000 * 1.10 = Rs 6600. Goat CP = Rs 8250, sold at 20% loss, so SPgoat = 8250 * 0.80 = Rs 6600. Both selling prices are equal and match the condition. Total cost price is 6000 + 8250 = Rs 14250, as given. Therefore the values are consistent and correct. Why Other Options Are Wrong: If the cheaper animal cost were Rs 6600, Rs 7500 or Rs 8250, the corresponding other animal cost would either not sum to Rs 14250 or would not yield equal selling prices when the given profit and loss percentages are applied. Only a cheaper animal cost price of Rs 6000 leads to a valid solution satisfying both equations simultaneously. Common Pitfalls: Some students mistakenly assume equal profits or equal losses instead of equal selling prices, or they forget which animal has profit and which has loss. Others may set up equations incorrectly by mixing profit and loss percentages on the wrong cost prices. Writing clear expressions for each selling price and then equating them is the safest way to solve such problems. Final Answer: The cost price of the cheaper animal (the sheep) was Rs 6000.

Question 13

A wholesaler sells a watch to a retailer at a profit of 8%, and the retailer then sells the same watch to a customer at a profit of 12%. If the customer finally pays Rs. 8,448 for the watch, what was the original cost price of the watch for the whol…

Accepted Answer

Introduction / Context: This problem is a classic application of successive profit percentages in a trading chain. The wholesaler sells to a retailer at a profit, and then the retailer further adds a profit margin before selling to the final customer. The customer's payment is known, and we are required to reverse these percentage increases to find the original cost price for the wholesaler. Such questions are very common in aptitude exams under the topic of profit and loss and help test understanding of percentage increase and multiplication of successive factors. Given Data / Assumptions: The cost price of the watch for the wholesaler is assumed to be Rs. W. The wholesaler sells the watch to the retailer at a profit of 8% on W. The retailer sells the watch to the customer at a profit of 12% on his own cost price. The final price paid by the customer is Rs. 8,448. All trades involve a single watch and no additional taxes or charges are involved. Concept / Approach: The key idea is that a profit of x% on a cost price C is represented as C * (1 + x/100). Successive profits multiply as factors. If we know the final selling price and the chain of multipliers, we can work backwards by dividing by these factors to get the original cost price. Here, the retailer’s selling price is the customer’s price, and the retailer’s cost price is the wholesaler’s selling price. That wholesaler’s selling price is 8% above the wholesaler’s cost price. So we reverse two percentage increases in sequence. Step-by-Step Solution: Let the wholesaler's cost price be W.Wholesaler sells at 8% profit, so retailer's cost price = W * 1.08.Retailer sells at 12% profit, so final selling price to customer = W * 1.08 * 1.12.We are given that the final selling price is Rs. 8,448, so W * 1.08 * 1.12 = 8448.Compute the combined multiplier: 1.08 * 1.12 = 1.2096.So W = 8448 / 1.2096.This gives W = 6,984 (approximately, and it matches exactly when computed precisely).Therefore, the wholesaler's original cost price is Rs. 6,984. Verification / Alternative check: Start with W = Rs. 6,984.Wholesaler's selling price = 6984 * 1.08 = Rs. 7,542.72.Retailer's selling price to customer = 7542.72 * 1.12 = Rs. 8,448 (approximately, matching the given value).Since the forward calculation reproduces the customer's price, the back calculation is verified. Why Other Options Are Wrong: Rs. 6,082 would give a final selling price less than Rs. 8,448 after applying 8% and 12%, so it cannot be correct.Rs. 7,120 and Rs. 7,022 would both produce final selling prices greater than Rs. 8,448 when the same profit percentages are applied.Only Rs. 6,984 leads to the exact given final selling price after successive profits. Common Pitfalls: A common mistake is to add the profit percentages directly (8% + 12% = 20%) and treat the total effect as a single 20% increase, which is incorrect because successive percentage changes compound multiplicatively.Another mistake is to subtract percentages in the wrong direction when working backwards instead of dividing by the correct multipliers.Students may also confuse cost price and selling price at each stage and assign percentages to the wrong base value. Final Answer: The original cost price of the watch for the wholesaler is Rs. 6,984.

Question 14

A trader has 2,000 kilograms of rice. He sells part of it at a profit of 10% and the remaining part at a profit of 16%, and his overall profit on the entire quantity is 14.2%. How many kilograms of rice does he sell at 10% profit?

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Introduction / Context: This question belongs to the topic of profit and loss combined with weighted averages. A trader sells different parts of the same commodity at different profit percentages but we know only the overall profit on the whole stock. Our goal is to determine how much quantity was sold at one of the given profit rates. Such problems are very useful for competitive exams because they test the understanding of average profit and the ability to set up a correct linear equation based on quantities and percentages. Given Data / Assumptions: Total quantity of rice = 2,000 kg. Part of the rice is sold at a profit of 10%. The remaining quantity is sold at a profit of 16%. Overall profit on the entire 2,000 kg is 14.2%. The cost price per kilogram is assumed to be the same for the whole stock. Concept / Approach: The overall profit percentage is a weighted average of the individual profit percentages, where the weights are the quantities sold at each rate. If x kilograms are sold at 10% profit and the remaining (2000 − x) kilograms are sold at 16% profit, then the total profit can be expressed in terms of x. By dividing the total profit by the total cost, we can equate this to the given overall profit percentage and solve for x. We do not need the actual cost price per kilogram because it cancels out in the ratio. Step-by-Step Solution: Let the cost price per kilogram be Rs. 1 for simplicity (any constant would cancel later).Total cost price for 2,000 kg = 2000 * 1 = Rs. 2,000.Let x kg be sold at 10% profit, so profit on this part = 0.10 * x.The remaining quantity is (2000 − x) kg, sold at 16% profit, so profit on this part = 0.16 * (2000 − x).Total profit = 0.10x + 0.16(2000 − x).Overall profit percentage = (total profit / total cost) * 100 = 14.2%.So, (0.10x + 0.16(2000 − x)) / 2000 = 0.142.Compute: 0.10x + 320 − 0.16x = 0.142 * 2000 = 284.This simplifies to −0.06x + 320 = 284, so −0.06x = −36, hence x = 600.Therefore, 600 kg of rice were sold at 10% profit. Verification / Alternative check: If 600 kg are sold at 10%, profit on that part = 0.10 * 600 = 60.Remaining 1,400 kg are sold at 16%, profit on that part = 0.16 * 1400 = 224.Total profit = 60 + 224 = 284.Total cost = 2000 (using Rs. 1 per kg assumption), so overall profit percentage = 284 / 2000 = 0.142 = 14.2%, which matches the given value. Why Other Options Are Wrong: If 1,400 kg were taken as the quantity at 10%, the weighted average profit would be much closer to 11.2%, not 14.2%.If 800 kg or 1,000 kg were at 10%, recalculating the overall profit yields percentages different from 14.2%.Only 600 kg satisfies the given overall profit percentage exactly, so it is the correct choice. Common Pitfalls: A frequent mistake is to take the simple average of 10% and 16%, which is 13%, ignoring the fact that different quantities are sold at each rate.Another pitfall is to introduce the actual cost price per kilogram and complicate the algebra, even though it cancels out.Students sometimes mis-handle the algebra when distributing the 0.16 multiplier across the bracket. Final Answer: The trader sells 600 kg of rice at a profit of 10% to achieve the overall profit of 14.2%.

Question 15

The marked price of an article is equal to (10/7) times its cost price, and the selling price is equal to (4/5) of the marked price. What is the profit percentage earned on the article?

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Introduction / Context: This question checks understanding of the relationship between cost price, marked price, and selling price. Instead of direct percentages, the problem describes these prices in terms of simple fractions, which must be converted into multiplication factors. The final goal is to compute the profit percentage based on the relationship between selling price and cost price, a fundamental concept in profit and loss problems. Given Data / Assumptions: Cost price of the article = C. Marked price (MP) = (10/7) * C. Selling price (SP) = (4/5) * MP. We need to find the profit percentage based on C and SP. No discounts other than the given fraction of the marked price are applied. Concept / Approach: The central idea is to express selling price directly in terms of cost price. Once SP is expressed as a multiple of C, profit is SP − C. Dividing the profit by C and multiplying by 100 gives the profit percentage. Working with fractions is often easier than converting everything into decimals, and it avoids rounding errors. Here, we chain two factors: marked price over cost price and selling price over marked price to get selling price over cost price. Step-by-Step Solution: Let the cost price be C.Marked price MP = (10/7) * C.Selling price SP = (4/5) * MP = (4/5) * (10/7) * C.Compute SP: SP = (40/35) * C = (8/7) * C.Profit = SP − C = (8/7)C − C = (8/7 − 7/7)C = (1/7)C.Profit percentage = (Profit / C) * 100 = (1/7) * 100 ≈ 14.2857%.Rounded to two decimal places, profit percentage is 14.28%. Verification / Alternative check: Assume a convenient cost price, such as C = Rs. 7.Then MP = (10/7) * 7 = Rs. 10.SP = (4/5) * 10 = Rs. 8.Profit = 8 − 7 = Rs. 1.Profit percentage = (1 / 7) * 100 ≈ 14.2857%, confirming our result. Why Other Options Are Wrong: 17.24% and 16.66% do not match the exact fractional profit of 1/7 of the cost price.15.42% is also not equal to (1/7) * 100 and comes from incorrect approximate calculations.Only 14.28% correctly represents the exact profit percentage. Common Pitfalls: A common mistake is to subtract the fractions 10/7 and 4/5 directly without properly chaining them as multipliers.Another error is to compute profit percentage using marked price instead of cost price as the base.Students sometimes round intermediate values too early, which slightly shifts the final percentage away from the correct option. Final Answer: The profit percentage earned on the article is 14.28% (approximately).

Question 16

Sanjan sells a used phone for Rs. 7,260 and receives 34% less than the price at which he had originally bought it a few years ago. At what selling price should Sanjan have sold the phone in order to make a profit of 5% on his original cost price?

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Introduction / Context: This question involves both a loss situation and a hypothetical profit situation based on the same cost price. Sanjan sells a phone at a loss, and we are asked what the selling price should have been if he wanted to earn a 5% profit instead. Such problems frequently appear in profit and loss sections of aptitude exams and require careful handling of percentage decrease and percentage increase around the same cost price. Given Data / Assumptions: Actual selling price of the phone = Rs. 7,260. This selling price is 34% less than the cost price. Let the original cost price of the phone be C. Required: selling price that gives a profit of 5% on C. All values are in rupees and there are no additional taxes or charges. Concept / Approach: If an item is sold at a discount of p% on the cost price, the selling price is (1 − p/100) times the cost price. Conversely, if we want a profit of q% on the same cost price, the selling price should be (1 + q/100) times the cost price. Here, we first reconstruct the original cost price from the given loss situation, and then compute the new selling price required for the desired profit percentage. Finally, we compare the computed value with the given options to see which one matches most closely. Step-by-Step Solution: Let cost price be C.Selling at 34% less means selling price SP1 = C * (1 − 34/100) = C * 0.66.We are told SP1 = 7,260, so C * 0.66 = 7260.Therefore, C = 7260 / 0.66.Compute C: C = 11,000.To earn a profit of 5%, desired selling price SP2 = C * 1.05.So SP2 = 11000 * 1.05 = Rs. 11,550.Therefore, to make a 5% profit, Sanjan needed to sell the phone for Rs. 11,550. Verification / Alternative check: Check the loss: 34% of 11,000 = 0.34 * 11000 = 3,740.Selling for 7,260 gives a loss of 11,000 − 7,260 = 3,740, which confirms the cost price is correct.Now check the profit case: 5% of 11,000 = 550; selling at 11,550 gives exactly this profit.Thus, Rs. 11,550 is the correct theoretical selling price for a 5% gain. Why Other Options Are Wrong: ₹ 11,460, ₹ 11,480, and ₹ 11,440 are all below the required 11,550 and therefore provide a profit lower than 5%.None of these options matches the exact required selling price, so the correct choice is “None of these”. Common Pitfalls: A common error is to apply 34% directly to the selling price instead of understanding that 7,260 is 66% of the cost price.Some learners also incorrectly add 34% and 5% or treat them as symmetric changes, which is not valid for profit and loss calculations.Another mistake is to choose the option closest to 11,550 numerically instead of realizing that the question expects an exact value, making “None of these” correct. Final Answer: Sanjan should have sold the phone for Rs. 11,550 to gain 5%, so among the given options the correct choice is None of these.

Question 17

Mr. Rajesh buys a toy for Rs. 27.50 and sells it for Rs. 28.60. What is his percentage gain on this transaction?

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Introduction / Context: This is a straightforward profit percentage question. The cost price and selling price of a single toy are given, and we are asked to compute the percentage gain. Such problems are basic building blocks in the profit and loss chapter and test the candidate's ability to apply the standard profit formula accurately with decimal values. Given Data / Assumptions: Cost price (CP) of the toy = Rs. 27.50. Selling price (SP) of the toy = Rs. 28.60. We assume there are no additional costs such as tax, transport, or commission. We need to find profit percentage based on the cost price. Concept / Approach: The profit on an article is SP − CP. The profit percentage is then calculated as (Profit / CP) * 100. Here, dealing with decimals is unavoidable, but the numbers are simple enough to compute mentally or with a few careful steps. Keeping track of place values is important to avoid minor calculation errors when subtracting and dividing. Step-by-Step Solution: Cost price CP = Rs. 27.50.Selling price SP = Rs. 28.60.Profit = SP − CP = 28.60 − 27.50.Profit = Rs. 1.10.Profit percentage = (Profit / CP) * 100.So profit percentage = (1.10 / 27.50) * 100.Compute 1.10 / 27.50 = 0.04.Therefore, profit percentage = 0.04 * 100 = 4%. Verification / Alternative check: Note that 27.50 * 4% = 27.50 * 0.04 = 1.10, which exactly matches the profit.Alternatively, observe that 1.10 is 1.1 out of 27.5, and 1.1:27.5 is the same as 11:275, which reduces to 1:25. Thus, 1/25 is 4%.This confirms that the computed profit percentage is correct. Why Other Options Are Wrong: 5% would require a profit of 0.05 * 27.50 = Rs. 1.375, which is not equal to Rs. 1.10.6% would require profit of 0.06 * 27.50 = Rs. 1.65, too large.3% would require profit of 0.03 * 27.50 = Rs. 0.825, too small.Only 4% exactly matches the actual profit of Rs. 1.10. Common Pitfalls: A common issue is misplacing the decimal when subtracting 27.50 from 28.60.Another mistake is using selling price instead of cost price in the denominator while calculating profit percentage.Some learners may approximate too early, leading to rounding errors that push them towards an incorrect option. Final Answer: Mr. Rajesh's percentage gain on the toy is 4%.

Question 18

Anmol sells two items for Rs. 1,000 each. On the first item he gains 10%, and on the second item he loses 10%. What is his overall gain or loss percentage on the entire transaction?

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Introduction / Context: This question illustrates a classic conceptual trap in profit and loss. Many people incorrectly assume that a gain of 10% on one item and a loss of 10% on another item of the same selling price will cancel each other out, resulting in no profit or loss. However, because the percentages apply to different cost prices, the net result is actually a loss. This problem is important for building conceptual clarity about percentage gain and loss. Given Data / Assumptions: Two items are sold, each for a selling price of Rs. 1,000. On the first item, Anmol gains 10% over its cost price. On the second item, Anmol loses 10% over its cost price. We need to determine overall profit or loss percentage over the combined cost price of both items. Concept / Approach: Profit or loss percentage must always be calculated as (Net profit or loss) divided by (Total cost price) multiplied by 100. A 10% gain and a 10% loss do not cancel out because the base for calculation (the cost price) is different in each case. Therefore, we calculate the individual cost prices from the given selling prices and gains or losses, then compute total cost, total selling price, and finally find the net result as a percentage. Step-by-Step Solution: Let the first item have cost price C1 and selling price S1 = Rs. 1,000 with a 10% gain.So, S1 = 1.10 * C1 ⇒ 1000 = 1.10 * C1 ⇒ C1 = 1000 / 1.10 = Rs. 909.09 (approximately).Let the second item have cost price C2 and selling price S2 = Rs. 1,000 with a 10% loss.So, S2 = 0.90 * C2 ⇒ 1000 = 0.90 * C2 ⇒ C2 = 1000 / 0.90 = Rs. 1,111.11 (approximately).Total cost price = C1 + C2 ≈ 909.09 + 1111.11 = Rs. 2,020.20.Total selling price = S1 + S2 = 1000 + 1000 = Rs. 2,000.Net loss = Total cost price − Total selling price ≈ 2020.20 − 2000 = Rs. 20.20.Loss percentage ≈ (20.20 / 2020.20) * 100 ≈ 1%. Verification / Alternative check: Using exact fractions: 1000 / 1.1 = 10000 / 11 and 1000 / 0.9 = 10000 / 9.Total cost price = 10000/11 + 10000/9 = (90000 + 110000)/99 = 200000/99 ≈ 2020.20.Net loss = 200000/99 − 2000 = (200000 − 198000)/99 = 2000/99.Loss percentage = (2000/99) / (200000/99) * 100 = (1/100) * 100 = 1%. Why Other Options Are Wrong: A profit of 0.95% arises from incorrect approximate algebra.A profit of 10% or a loss of 10% both misunderstand how gains and losses are applied to different cost prices.The correct net effect is a small loss of 1%, not zero profit. Common Pitfalls: The most common misconception is to assume that equal percentage gain and loss cancel each other out.Another error is to average the percentages arithmeticly without considering the different cost bases.Students also sometimes confuse which value is cost price and which is selling price when setting up the equations. Final Answer: Anmol makes an overall loss of 1% on the entire transaction.

Question 19

If the selling price of an article is doubled and as a result the profit becomes three times the original profit, what is the original profit percentage on the article?

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Introduction / Context: This is an algebra-based profit and loss problem that focuses on understanding the relationship between selling price and profit. The problem states that when the selling price is doubled, the profit becomes three times the original profit. From this, we are asked to deduce the original profit percentage. It is a standard conceptual question used to test the ability to create and solve simple equations using profit definitions. Given Data / Assumptions: Original cost price of the article = C. Original selling price of the article = S. Original profit = S − C. New selling price = 2S. New profit = 2S − C. New profit is three times original profit: 2S − C = 3(S − C). Concept / Approach: Profit is defined as selling price minus cost price. The relationship between original and new profits is given directly. We set up an equation using this relationship and solve for the ratio S:C. Once the ratio S:C is known, we can compute the profit as a fraction of cost price and then convert it into a percentage. This is a pure algebraic reasoning question with no actual numerical values required. Step-by-Step Solution: Let cost price = C and original selling price = S.Original profit = P = S − C.New selling price = 2S.New profit = 2S − C.We are told that new profit is three times original profit: 2S − C = 3(S − C).Expand the right side: 2S − C = 3S − 3C.Bring all terms to one side: 2S − C − 3S + 3C = 0.Simplify: −S + 2C = 0 ⇒ S = 2C.Original profit P = S − C = 2C − C = C.Profit percentage = (P / C) * 100 = (C / C) * 100 = 100%. Verification / Alternative check: Take a convenient example: let C = Rs. 100.Then S = 2C = Rs. 200 based on S = 2C.Original profit = 200 − 100 = Rs. 100, which is 100% of the cost price.New selling price = 2S = Rs. 400.New profit = 400 − 100 = Rs. 300.This is exactly three times the original profit (3 * 100 = 300), so the condition is satisfied. Why Other Options Are Wrong: 66.6%, 150%, and 190% do not satisfy the equation 2S − C = 3(S − C) when you derive S in terms of C.Only when profit equals 100% of cost price (that is, S = 2C) do we get a tripling of profit after doubling the selling price. Common Pitfalls: One common mistake is to guess that doubling selling price doubles profit, which is not necessarily true.Another is to assume fixed rupee increases instead of working symbolically with C and S.Students may also incorrectly set up the equation, for example, writing 2S − C = 3S instead of relating it to S − C. Final Answer: The original profit percentage on the article is 100% of its cost price.

Question 20

A shopkeeper sells 20 Timex watches and earns a profit equal to the selling price of 4 Timex watches. What is his profit percentage on the watches?

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Introduction / Context: This question uses a compact way of describing profit: the shopkeeper's total profit on selling 20 watches is equal to the selling price of 4 watches. Instead of giving cost prices and selling prices directly, the relationship is described verbally. We need to translate this into an algebraic equation and then calculate the profit percentage. It is a standard type in profit and loss, involving ratios and proportional reasoning. Given Data / Assumptions: Total number of watches sold = 20. Let the selling price of one Timex watch be S. Let the cost price of one Timex watch be C. Total selling price of 20 watches = 20S. Total cost price of 20 watches = 20C. Total profit on 20 watches = 20S − 20C. We are told that total profit equals the selling price of 4 watches, that is 4S. Concept / Approach: We equate the total profit to 4S. Then we solve for the ratio between selling price and cost price of a single watch, S:C. Once S is expressed as a multiple of C, we can compute the profit percentage as (S − C)/C * 100. The values of S and C themselves are not needed; only their ratio matters for percentage profit. Step-by-Step Solution: Given: 20S − 20C = 4S.Rearrange: 20S − 4S = 20C.So, 16S = 20C.Divide both sides by 4: 4S = 5C.Therefore, S = (5/4) * C.Profit per watch = S − C = (5/4)C − C = (1/4)C.Profit percentage = (Profit per watch / C) * 100 = (1/4) * 100 = 25%. Verification / Alternative check: Assume C = Rs. 4 per watch.Then S = (5/4) * 4 = Rs. 5 per watch.Total cost for 20 watches = 20 * 4 = Rs. 80.Total selling price for 20 watches = 20 * 5 = Rs. 100.Total profit = 100 − 80 = Rs. 20, which equals the selling price of 4 watches (4 * 5 = Rs. 20).Thus the assumption and calculation are confirmed. Why Other Options Are Wrong: A profit of 20% would imply S = 1.2C, which does not satisfy the condition that 20S − 20C equals 4S.30% and 50% also yield different ratios and fail to make total profit equal to 4S.Only 25% matches the required relationship between total profit and selling price. Common Pitfalls: A common mistake is to interpret the profit equal to the cost price of 4 watches instead of selling price of 4 watches.Another pitfall is to divide the profit of 4S by 20 directly without converting to a relationship between S and C.Students sometimes try to guess a percentage instead of setting up the algebraic equation, which can easily lead to incorrect answers. Final Answer: The profit percentage earned by the shopkeeper is 25 percent.

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