Question 1

A trader sells an article at a profit of 20% on its cost price. Had he bought that article at a price 60% lower than its original cost price and sold it for Rs. 90 less than the original selling price, he would have gained 50%. What is the original …

Accepted Answer

Introduction / Context: This is a slightly tricky profit and loss problem where both the cost price and selling price are changed in a hypothetical scenario. Originally, the trader earns a 20% profit. In a second scenario, he imagines buying the article cheaper (60% less cost) and selling it for Rs. 90 less than the original selling price, resulting in a 50% profit. Using these conditions, we must determine the original cost price of the article. Given Data / Assumptions: Let the original cost price (CP) be x rupees. Original profit percentage = 20%. Original selling price SP1 = 1.20x. In the hypothetical scenario, cost price CP2 = x − 60% of x = 0.40x. New selling price SP2 = SP1 − 90 = 1.20x − 90. In this scenario, profit percentage = 50%, so SP2 = 1.50 * CP2. Concept / Approach: We form an equation by equating the new selling price from the narrative description (1.20x − 90) to the selling price expression derived from the 50% profit condition (1.5 * 0.40x). This gives a simple linear equation in x. Solving that equation yields the original cost price. This method ensures both scenarios are correctly captured in one mathematical relationship. Step-by-Step Solution: Let the original cost price be x rupees. Original selling price SP1 = 1.20x (because profit is 20%). In the second scenario, new cost price CP2 = 40% of x = 0.40x. New selling price SP2 is Rs. 90 less than SP1, so SP2 = 1.20x − 90. This SP2 gives a profit of 50% on CP2, so SP2 = 1.50 * CP2. Therefore, 1.20x − 90 = 1.50 * 0.40x. Compute the right-hand side: 1.50 * 0.40x = 0.60x. So the equation becomes: 1.20x − 90 = 0.60x. Rearrange: 1.20x − 0.60x = 90. 0.60x = 90. x = 90 / 0.60 = 150. Thus, the original cost price of the article is Rs. 150. Verification / Alternative check: With CP = 150, original SP1 = 1.20 * 150 = Rs. 180. In the second scenario, CP2 = 40% of 150 = Rs. 60. SP2 calculated from the condition is SP1 − 90 = 180 − 90 = Rs. 90. Profit in the second scenario = 90 − 60 = Rs. 30. Profit percentage = (30 / 60) * 100 = 50%, which matches the problem statement. Therefore, CP = Rs. 150 is consistent with both scenarios. Why Other Options Are Wrong: 200, 250, 300 and 180: Substituting any of these values for x fails to satisfy the relationship 1.20x − 90 = 0.60x, and the 50% profit condition breaks. For example, if x = 200, then SP1 = 240 and SP2 = 150, while CP2 = 80. Profit = 70, which is not 50% of 80. Common Pitfalls: Students sometimes confuse “bought at 60% less price” with “bought at 60% of the original price,” which is wrong. The phrase “60% less” means 40% of the original price, not 60%. Another error is to ignore the requirement that SP2 has to be Rs. 90 less than SP1 and instead relate SP2 directly to CP without using the original selling price. Writing the equations clearly from the wording helps avoid misinterpretation. Final Answer: The original cost price of the article is Rs. 150.

Question 2

Amit donates 20% of his monthly income to a school and then deposits 20% of the remaining amount in his bank account. After these two actions, he is left with Rs. 12,800. What is Amit's total monthly income in rupees?

Accepted Answer

Introduction / Context: This is a typical percentage and income-based word problem. Amit spends part of his income on donation and savings in a bank. The problem describes two consecutive percentage deductions from his initial income and tells us how much money remains afterwards. We must work backwards to find his original monthly income. Such questions test understanding of successive percentage operations and the idea of working in reverse from a final amount. Given Data / Assumptions: Let Amit's monthly income be I rupees. He donates 20% of I to a school. He then deposits 20% of the remaining amount in his bank. After donation and deposit, he is left with Rs. 12,800. We must find the value of I. Concept / Approach: The key idea is to carefully track the remaining percentage of income after each operation. First, donating 20% leaves 80% of the income. Then, depositing 20% of that remainder leaves 80% of the remainder. Overall, he keeps 80% of 80% of his original income, which is 64% of I. This final amount is given as Rs. 12,800, so we set 0.64I = 12,800 and solve for I. This approach is much faster and less error-prone than guessing values. Step-by-Step Solution: Let Amit's monthly income be I rupees. He donates 20% of I, so donation = 0.20I. Amount left after donation = I − 0.20I = 0.80I. He deposits 20% of the remaining amount in his bank. Deposit amount = 20% of 0.80I = 0.20 * 0.80I = 0.16I. Amount left after deposit = 0.80I − 0.16I = 0.64I. We are told that this remaining amount equals Rs. 12,800. So, 0.64I = 12,800. Therefore, I = 12,800 / 0.64. 0.64 = 64 / 100, so I = 12,800 * 100 / 64. Compute 12,800 / 64 = 200. Thus, I = 200 * 100 = Rs. 20,000. Verification / Alternative check: Starting from Rs. 20,000, donation at 20% is 0.20 * 20,000 = Rs. 4,000. Remaining amount = 20,000 − 4,000 = Rs. 16,000. Deposit is 20% of 16,000, which equals 0.20 * 16,000 = Rs. 3,200. Amount left after deposit = 16,000 − 3,200 = Rs. 12,800, which matches the amount stated in the question. Hence the calculated income is correct. Why Other Options Are Wrong: 18,000 and 16,000: These would leave significantly less than Rs. 12,800 after deducting the two percentages. 24,000 and 32,000: These would leave more than Rs. 12,800 after operations, and do not satisfy the equation 0.64I = 12,800. Common Pitfalls: A common error is to subtract 40% directly from the income and assume that the remainder is 60%, ignoring that the second 20% is taken on the already reduced amount, not on the original income. Another mistake is to add the percentages incorrectly. Always express successive percentage changes as multipliers (like 0.80 * 0.80) and then apply them to the original amount or work backwards from the final amount to the original. Final Answer: Amit's total monthly income is Rs. 20,000.

Question 3

The marked price of an article is 20% more than its cost price. If a shopkeeper gives a discount of 5% on the marked price, what is the profit percentage earned on the cost price?

Accepted Answer

Introduction / Context: This question combines the concepts of marked price, discount and profit. The article is first marked up over its cost price and then a discount is given on that marked price. Even after giving the discount, the shopkeeper still makes a profit. We must compute the final profit percentage on the cost price after both operations. Given Data / Assumptions: Let the cost price (CP) of the article be C rupees. Marked price (MP) is 20% more than CP, i.e., MP = 1.20C. Discount given on MP = 5%. We must find the profit percentage on C after applying the discount. Concept / Approach: First, we calculate the selling price by applying the discount to the marked price. Selling price SP = MP * (1 − discount). Once SP is known in terms of C, the profit is SP − CP and the profit percentage is (SP − CP) / CP * 100. Since both operations are simple percentages, the algebra remains straightforward. Step-by-Step Solution: Assume cost price = C rupees. Marked price MP is 20% more than C, so MP = C * 1.20 = 1.20C. Discount on marked price = 5%. Therefore, selling price SP = MP * (1 − 0.05) = 1.20C * 0.95. SP = 1.140C. Profit = SP − CP = 1.140C − C = 0.140C. Profit percentage = (Profit / CP) * 100. Profit percentage = (0.140C / C) * 100 = 14%. Verification / Alternative check: Let C = Rs. 100 for an easy check. Then MP = 120% of 100 = Rs. 120. Discount of 5% on MP means discount amount = 5% of 120 = Rs. 6. New selling price SP = 120 − 6 = Rs. 114. Profit = SP − CP = 114 − 100 = Rs. 14. Profit percentage = (14 / 100) * 100 = 14%. This confirms that the calculated percentage is correct. Why Other Options Are Wrong: 5% and 10%: These underestimate the true profit because they effectively treat the net increase incorrectly after markup and discount. 15% and 25%: These overestimate the profit. 25% would correspond to keeping the full 20% markup without discount plus extra, which is not the case here. Common Pitfalls: One common mistake is to add or subtract percentages directly, for example computing 20% − 5% = 15% and concluding that profit is 15%. This ignores the fact that 5% discount is calculated on the marked price, which is itself 20% higher than cost. The correct method is to multiply the successive percentage factors, 1.20 and 0.95, and then compare with 1.00 (the cost price base). Final Answer: The shopkeeper earns a profit of 14% on the cost price.

Question 4

A person buys pens at the rate of 25 pens for one rupee and later sells them at the rate of 15 pens for one rupee. What is his profit percentage on the transaction?

Accepted Answer

Introduction / Context: This question deals with buying and selling items in different quantity-rate forms, a very common pattern in profit and loss problems. The person buys pens at a rate of 25 for Re. 1 and sells them at a rate of 15 for Re. 1. Since the cost and selling rates are expressed as “number of pens per rupee,” we must convert them into cost per pen and selling price per pen, then compute profit and profit percentage. Given Data / Assumptions: Buying rate: 25 pens for Re. 1. Selling rate: 15 pens for Re. 1. We assume large enough quantity so that the rates hold exactly. We need the profit percentage on cost price. Concept / Approach: To find profit percentage, we need cost price and selling price per pen. From “25 pens for Re. 1” we get cost per pen. From “15 pens for Re. 1” we get selling price per pen. Profit per pen is the difference between selling price and cost price. Profit percentage is then (profit per pen / cost price per pen) * 100. The actual number of pens transacted does not matter because the ratio remains the same. Step-by-Step Solution: Cost for 25 pens = Re. 1. Therefore, cost price (CP) per pen = 1 / 25 rupee. Selling price for 15 pens = Re. 1. Therefore, selling price (SP) per pen = 1 / 15 rupee. Profit per pen = SP − CP = (1 / 15) − (1 / 25). Compute (1 / 15) − (1 / 25) = (25 − 15) / (15 * 25) = 10 / 375 = 2 / 75. So, profit per pen = 2 / 75 rupee. Cost price per pen = 1 / 25 = 3 / 75 rupee. Profit percentage = (profit per pen / cost price per pen) * 100. Profit percentage = ( (2 / 75) / (3 / 75) ) * 100. The 75 cancels out, giving (2 / 3) * 100. (2 / 3) * 100 = 66.67% (approximately), which is 66 2/3 percent. Verification / Alternative check: Take a convenient total number of pens, for example 75 pens. At the buying rate of 25 for Re. 1, cost for 75 pens = 3 rupees. At the selling rate of 15 for Re. 1, 75 pens will be sold in 5 groups of 15, so selling price = 5 rupees. Profit = 5 − 3 = 2 rupees. Profit percentage = (2 / 3) * 100 ≈ 66.67%, matching our earlier calculation. Why Other Options Are Wrong: 16 2/3 and 33 1/3: These are much lower profit percentages and would arise if one incorrectly averaged rates or miscomputed per-pen amounts. 40 and 50: These are plausible but do not match the exact ratio 2 / 3 of cost. A quick numerical check with 75 pens shows that these percentages are not correct. Common Pitfalls: A typical mistake is to compare only the numbers 25 and 15 and conclude that the profit is (25 − 15) / 25 = 40%, which is wrong because the base should be cost per pen, not number of pens. Another error is to use rupees per pen instead of pens per rupee interchangeably without converting properly. Always convert both buying and selling rates to per-unit cost and then proceed to find profit percentage. Final Answer: The person makes a profit of approximately 66.67% on the pens.

Question 5

A shopkeeper offers a cash discount of 2.5% on the marked price of a cycle. If the marked price of the cycle is Rs. 3,600, what cash amount does Rohit have to pay to buy the cycle?

Accepted Answer

Introduction / Context: This is a straightforward discount calculation problem. The shopkeeper offers a small discount on the marked price of a cycle for cash payment. The question asks for the actual amount that Rohit must pay after the discount is applied. Such questions are basic but important building blocks in understanding percentage-based price reductions in commerce and daily life. Given Data / Assumptions: Marked price (MP) of the cycle = Rs. 3,600. Cash discount offered = 2.5% of the marked price. Rohit pays the discounted price in cash. We need to find the final amount paid by Rohit. Concept / Approach: We use the basic discount formula: Discount amount = (discount percentage / 100) * marked price. Then, selling price or cash price = marked price − discount amount. Since the percentage is small (2.5%), the arithmetic is simple. We must take care to compute 2.5% accurately and subtract it from the marked price. Step-by-Step Solution: Marked price MP = Rs. 3,600. Discount rate = 2.5%. Discount amount = (2.5 / 100) * 3,600. 2.5 / 100 = 0.025. Discount amount = 0.025 * 3,600. 0.025 * 3,600 = 90. So, discount amount = Rs. 90. Cash price Rohit has to pay = MP − discount amount. Cash price = 3,600 − 90 = Rs. 3,510. Verification / Alternative check: An alternative view is to directly find 97.5% of the marked price, because giving a 2.5% discount means Rohit pays 100% − 2.5% = 97.5% of the price. Then cash price = 0.975 * 3,600. Calculating: 0.975 * 3,600 = 3,510. This matches the result obtained by computing the discount separately, confirming that Rs. 3,510 is correct. Why Other Options Are Wrong: 3,490 and 3,500: These correspond to slightly larger discounts than 2.5% (around 3% or more), not the exact rate given. 3,520: This amount is too high and corresponds to a discount of only Rs. 80, which is less than 2.5%. 3,450: This would require a larger discount of Rs. 150, which is more than 4%. Common Pitfalls: Sometimes students misread 2.5% as 25% and compute a much larger discount. Others forget to divide by 100 when converting a percentage to a decimal. It is also easy to make arithmetic mistakes when multiplying 0.025 by 3,600, so doing the calculation stepwise, for example 1% of 3,600 is 36, so 2.5% is 2.5 * 36 = 90, helps avoid errors. Final Answer: Rohit has to pay a cash amount of Rs. 3,510 for the cycle.

Question 6

If rice is sold at Rs. 56 per kilogram, the shopkeeper incurs a loss of 40% on the cost price. To earn a profit of 20% instead, at what price per kilogram should he sell the rice?

Accepted Answer

Introduction / Context: This question explores how the selling price of a commodity affects whether the seller incurs a loss or gains a profit. Initially, selling rice at a given price leads to a 40% loss. We are then asked to find the new selling price that would instead yield a 20% profit on the same cost price. It is a classic example of working with loss and profit percentages to find correct selling prices in aptitude exams. Given Data / Assumptions: When sold at Rs. 56 per kg, there is a loss of 40%. Let the cost price (CP) per kg be C. Loss of 40% means selling price SP1 = 0.60C = Rs. 56. We want a profit of 20%, so desired selling price SP2 = 1.20C. We must find SP2 in rupees per kilogram. Concept / Approach: First, we determine the cost price from the loss scenario. A 40% loss implies that selling price is 60% of cost price. From SP1 = 0.60C = 56, we solve for C. Once C is known, calculating the selling price for a 20% profit is straightforward using SP2 = 1.20C. This stepwise approach keeps the logic clear and avoids confusion between loss and profit percentages. Step-by-Step Solution: Let cost price per kg be C rupees. A loss of 40% means selling price SP1 = 60% of CP = 0.60C. We are told SP1 = Rs. 56. So, 0.60C = 56. Therefore, C = 56 / 0.60. 56 / 0.60 = 56 * (100 / 60) / 100 = 5600 / 60 = 280 / 3 ≈ 93.33. Now we want a profit of 20%, so new selling price SP2 = 1.20C. SP2 = 1.20 * (280 / 3). 1.20 = 6 / 5, so SP2 = (6 / 5) * (280 / 3) = (6 * 280) / (15). 6 * 280 = 1,680. So SP2 = 1,680 / 15 = 112. Hence, the new selling price should be Rs. 112 per kg. Verification / Alternative check: Using C = 280 / 3 ≈ 93.33, selling at Rs. 56 gives loss = 93.33 − 56 ≈ 37.33. Loss percentage ≈ (37.33 / 93.33) * 100 ≈ 40%, confirming the first condition. At the new selling price Rs. 112, profit = 112 − 93.33 ≈ 18.67. Profit percentage ≈ (18.67 / 93.33) * 100 ≈ 20%, confirming the second condition. Why Other Options Are Wrong: 108 and 116: These are close values but when checked, they do not yield exactly 20% profit on the calculated cost price. 124: This gives a profit greater than 20% and does not satisfy the condition exactly. 96: This price is only slightly above the cost price and corresponds to a much smaller profit percentage. Common Pitfalls: A frequent error is to directly add 40% and 20%, mistakenly thinking the new price is some simple percentage of the old selling price. Another mistake is to compute cost price incorrectly by treating 56 as 40% of C instead of 60%. The correct interpretation is that after a 40% loss, the seller receives only 60% of the cost price as selling price. Getting this relationship right is crucial. Final Answer: To earn a 20% profit, the shopkeeper should sell the rice at Rs. 112 per kilogram.

Question 7

The marked price of a chair is Rs. 550. If a discount of 20% is allowed on the marked price, what is the selling price of the chair in rupees?

Accepted Answer

Introduction / Context: This is a basic discount and selling price question involving a single article, a chair. The shopkeeper reduces the price of the chair by a given percentage of the marked price and we must compute the final selling price after the discount. Such questions commonly appear at the introductory level of profit, loss and discount topics in aptitude tests. Given Data / Assumptions: Marked price (MP) of the chair = Rs. 550. Discount offered = 20% of the marked price. We must find the selling price after allowing this discount. Concept / Approach: The discount amount is calculated as a percentage of the marked price. The selling price is then the difference between the marked price and the discount amount. Mathematically: Discount = (discount rate / 100) * MP, and Selling price = MP − Discount. Alternatively, we can multiply the marked price directly by (1 − discount rate) to get the selling price. Step-by-Step Solution: Marked price MP = Rs. 550. Discount rate = 20%. Discount amount = (20 / 100) * 550. 20 / 100 = 0.20. Discount amount = 0.20 * 550 = Rs. 110. Selling price SP = MP − Discount. SP = 550 − 110 = Rs. 440. Verification / Alternative check: Instead of first finding the discount, we could directly calculate 80% of the marked price because selling price after a 20% discount is 100% − 20% = 80% of MP. Then SP = 0.80 * 550 = 440, giving the same result. This confirms that the calculation is consistent and correct. Why Other Options Are Wrong: 430 and 420: These represent larger discounts than 20% and would correspond to discount rates higher than 20% if checked numerically. 470: This would correspond to a discount of only Rs. 80, which is less than 20%. 390: This is far below the correct price and corresponds to a discount greater than 28% of the marked price. Common Pitfalls: Some students mistakenly subtract 20 rupees instead of 20% or miscalculate 20% of 550. Another error is to directly subtract 20% from 550 as if it were a fixed amount, not realizing that percentages always refer to parts of the base value. Writing out the step of computing discount as 0.20 * 550 helps avoid confusion. Final Answer: The selling price of the chair after allowing a 20% discount is Rs. 440.

Question 8

A trader sells two items at Rs. 400 each. On the first item he gains 15%, and on the second item he loses 15%. What is the trader's net loss on the whole transaction in rupees?

Accepted Answer

Introduction / Context: This question involves equal selling prices with opposite profit and loss percentages on two different items. The trader sells both items at the same selling price, one at a gain and the other at a loss of equal percentage. It is a well known result that when equal percentage profit and loss occur on equal selling prices (or equal cost prices in another variant), the overall result is a loss. We must compute the exact net loss amount in rupees for this specific situation. Given Data / Assumptions: Selling price (SP) of each item = Rs. 400. First item: profit = 15%. Second item: loss = 15%. We must find the net loss in rupees over both items combined. Concept / Approach: Let the cost prices of the two items be CP1 and CP2. For the first item, SP1 = 1.15 * CP1. For the second item, SP2 = 0.85 * CP2. Given that SP1 = SP2 = Rs. 400, we can find CP1 and CP2 separately. Then, total cost price is CP1 + CP2 and total selling price is SP1 + SP2 = Rs. 800. The difference between total cost price and total selling price gives the net loss, which we then interpret numerically. Step-by-Step Solution: Let CP1 be the cost price of the first item and CP2 the cost price of the second item. For the first item: SP1 = 1.15 * CP1 and SP1 = Rs. 400. So, 1.15 * CP1 = 400. CP1 = 400 / 1.15 ≈ 347.83. For the second item: SP2 = 0.85 * CP2 and SP2 = Rs. 400. So, 0.85 * CP2 = 400. CP2 = 400 / 0.85 ≈ 470.59. Total cost price = CP1 + CP2 ≈ 347.83 + 470.59 = 818.42 (approximately). Total selling price = SP1 + SP2 = 400 + 400 = 800. Net loss = Total CP − Total SP ≈ 818.42 − 800 = 18.42 (approximately). Rounded to two decimal places, net loss ≈ Rs. 18.41. Verification / Alternative check: We can check with more exact fractions. CP1 = 400 / 1.15 = 40000 / 115 ≈ 347.826. CP2 = 400 / 0.85 = 40000 / 85 ≈ 470.588. Total CP = (40000 / 115) + (40000 / 85). Computing numerically again gives about 818.414. Subtracting 800 from this total yields approximately 18.414 rupees, which matches the closest option Rs. 18.41. Why Other Options Are Wrong: 22.14, 20.25, 24.36 and 16.80: These all represent different loss amounts that do not match the precise calculation based on the given percentages and selling prices. If substituted into reverse calculations, none of them lead back to consistent 15% profit and 15% loss values at a selling price of Rs. 400 for each item. Common Pitfalls: A common misconception is to think the profit and loss cancel out because the percentages are the same in magnitude. They do not cancel, because they are applied on different base cost prices, not on the same amount. Another mistake is to incorrectly average the percentages and conclude zero net effect. Always compute cost prices individually using SP = CP * (1 ± percentage) and then compare total cost and total sales. Final Answer: The trader incurs a net loss of approximately Rs. 18.41 on the whole transaction.

Question 9

If an article is sold at a gain of 6% instead of a loss of 6%, the seller receives Rs. 6 more in selling price. What is the cost price of the article in rupees?

Accepted Answer

Introduction / Context: This is a classic profit and loss question where replacing a loss with a gain of the same percentage changes the selling price by a known rupee amount. The key observation is that the difference between a 6% gain and a 6% loss is a total change of 12% of the cost price. Knowing the rupee difference in selling price allows us to compute the cost price directly. Given Data / Assumptions: If sold at 6% loss, there is one selling price. If sold at 6% gain, there is another selling price. Difference between these two selling prices = Rs. 6. Let cost price (CP) of the article be C rupees. Concept / Approach: At a loss of 6%, selling price SP1 = 0.94C. At a gain of 6%, selling price SP2 = 1.06C. The difference SP2 − SP1 equals 1.06C − 0.94C = 0.12C, which is 12% of C. The problem states that this difference equals Rs. 6. Therefore, 0.12C = 6, from which we can solve for C directly, giving the cost price. Step-by-Step Solution: Let cost price of the article be C rupees. Selling price at 6% loss: SP1 = C * (1 − 6 / 100) = 0.94C. Selling price at 6% gain: SP2 = C * (1 + 6 / 100) = 1.06C. Difference between the two selling prices: SP2 − SP1 = 1.06C − 0.94C. SP2 − SP1 = 0.12C. Given that this difference equals Rs. 6. So, 0.12C = 6. Therefore, C = 6 / 0.12. Compute 6 / 0.12 = 50. Thus, the cost price of the article is Rs. 50. Verification / Alternative check: Check with C = Rs. 50. At 6% loss, SP1 = 0.94 * 50 = Rs. 47. At 6% gain, SP2 = 1.06 * 50 = Rs. 53. Difference SP2 − SP1 = 53 − 47 = Rs. 6, which matches the given condition. Hence C = 50 is fully consistent with the problem statement. Why Other Options Are Wrong: 18, 36, 42 and 60: For each of these cost prices, the difference between 6% gain and 6% loss would be 12% of the chosen value. In each case, 12% of that value is not equal to 6 rupees. For example, for 60, 12% of 60 is 7.2, not 6. Common Pitfalls: A common error is to treat the difference in percentages (6% and −6%) as 6% instead of 12%. The gain and loss act in opposite directions, so the total change in percentage is 6% + 6% = 12%. Another mistake is to misinterpret “gain instead of loss” and set up only one selling price expression. Always write both selling price formulas and subtract them to form the correct equation. Final Answer: The cost price of the article is Rs. 50.

Question 10

A vendor buys bananas at the rate of 12 for Rs. 50 and sells them at the rate of 5 for Rs. 40. What is his profit percentage on the transaction?

Accepted Answer

Introduction / Context: This question is another example of buying and selling goods at different quantity-based price rates, common in profit and loss problems. The vendor buys bananas at a certain rate (12 for Rs. 50) and sells them at a much higher rate (5 for Rs. 40). The task is to calculate the percentage profit on the cost price by converting these rates into per-banana cost price and per-banana selling price. Given Data / Assumptions: Buying rate: 12 bananas for Rs. 50. Selling rate: 5 bananas for Rs. 40. We can assume a large number of bananas keeping the same rates. We must find the profit percentage on the cost price. Concept / Approach: The approach is to calculate the cost price per banana and the selling price per banana. Profit per banana is the difference between selling and cost prices. The profit percentage is then (profit per banana / cost price per banana) * 100. This method is independent of the actual number of bananas and relies only on the ratio of total cost to total quantity. Step-by-Step Solution: Cost for 12 bananas = Rs. 50. Cost price (CP) per banana = 50 / 12 rupees. Selling price for 5 bananas = Rs. 40. Selling price (SP) per banana = 40 / 5 = Rs. 8. Compute CP per banana: CP = 50 / 12 ≈ 4.1667 rupees. Profit per banana = SP − CP = 8 − (50 / 12). 8 = 96 / 12, so profit per banana = (96 / 12) − (50 / 12) = 46 / 12. Simplify 46 / 12 = 23 / 6 ≈ 3.8333 rupees. Profit percentage = (profit per banana / CP per banana) * 100. Profit percentage = ( (23 / 6) / (50 / 12) ) * 100. (23 / 6) / (50 / 12) = (23 / 6) * (12 / 50) = (23 * 12) / (6 * 50). (23 * 12) / (6 * 50) = (23 * 2) / 50 = 46 / 50 = 0.92. Therefore, profit percentage = 0.92 * 100 = 92%. Verification / Alternative check: Take a convenient total number, for example 60 bananas. At the buying rate, 12 bananas cost Rs. 50, so 60 bananas (5 groups of 12) cost 5 * 50 = Rs. 250. At the selling rate, 5 bananas sell for Rs. 40, so 60 bananas (12 groups of 5) sell for 12 * 40 = Rs. 480. Profit = 480 − 250 = Rs. 230. Profit percentage = (230 / 250) * 100 = 92%, which confirms our calculation. Why Other Options Are Wrong: 82, 72, 62 and 68: These are all smaller than the actual profit percentage. They might result from partial simplification, using wrong denominators or incorrectly converting between the buy and sell rates. A quick check with 60 bananas, as shown above, clearly gives 92%, not any of these other values. Common Pitfalls: One frequent mistake is to compare 12 and 5 directly and assume a simple ratio-based profit without converting to monetary cost per unit. Another is to accidentally compute profit on the selling price instead of on the cost price. It is also easy to make algebraic errors when simplifying fractions; using a convenient total number of bananas is often the safest strategy. Final Answer: The vendor makes a profit of 92% on the bananas.

Question 11

Mahesh buys a watch with a marked price of Rs. 300 and offers the buyer two successive discounts of 15% and 6% on this marked price. What will be the final selling price of the watch in rupees after both discounts are applied?

Accepted Answer

Introduction / Context: This problem tests the concept of successive discounts applied on a marked price. Mahesh has a watch with a marked price of Rs. 300 and gives two consecutive discounts, first 15% and then 6%, to the buyer. Successive percentage changes must be handled multiplicatively rather than additively, which is the key idea behind this question. We must compute the combined effect of the two discounts to determine the final selling price. Given Data / Assumptions: Marked price (MP) of the watch = Rs. 300. First discount = 15% of the marked price (applied first). Second discount = 6% of the price after the first discount. We must find the final selling price after applying both discounts. Concept / Approach: Successive discounts are applied step by step. After a 15% discount, the price becomes 85% of the original marked price. Then a further 6% discount is applied on this reduced price, making the final selling price 94% of the new intermediate price. Algebraically, the final price is MP * (1 − 0.15) * (1 − 0.06). We then plug in MP = 300 and compute the result. Step-by-Step Solution: Marked price MP = Rs. 300. First discount = 15%. Price after first discount = MP * (1 − 0.15) = 300 * 0.85. 300 * 0.85 = Rs. 255. Second discount = 6% on the reduced price. Price after second discount = 255 * (1 − 0.06) = 255 * 0.94. Compute 255 * 0.94 = 255 * (94 / 100) = (255 * 94) / 100. 255 * 94 = 23,970. So final selling price SP = 23,970 / 100 = Rs. 239.70. Rounded to one decimal place, SP ≈ Rs. 239.7. Verification / Alternative check: We can also combine the discounts multiplicatively. Overall factor after two successive discounts of 15% and 6% is (1 − 0.15) * (1 − 0.06) = 0.85 * 0.94 = 0.799. Thus, final price = 300 * 0.799 = Rs. 239.7. This matches the detailed stepwise calculation, confirming that our answer is correct. Why Other Options Are Wrong: 213.4 and 225.0: These correspond to larger effective overall discounts than 1 − 0.799 = 20.1%. 242.3 and 247.4: These represent smaller overall discounts and are not equal to the result of applying 15% then 6% exactly. Only Rs. 239.7 matches the exact product 300 * 0.85 * 0.94. Common Pitfalls: A frequent error is to add the discount percentages and treat them as a single 21% discount on Rs. 300, giving price = 300 * 0.79 = Rs. 237, which is incorrect. Successive discounts must always be applied stepwise because each percentage is taken on a different base amount. Another mistake is to round intermediate values too early, which can slightly distort the final result. Retaining a few extra decimal places until the final step helps maintain accuracy. Final Answer: The selling price of the watch after two successive discounts is Rs. 239.7.

Question 12

A merchant offers a discount of 30% on the list price of an article and as a result incurs a loss of 16% on the cost price. If instead the merchant offers a discount of 20% on the same list price, what percentage profit or loss will be made on the c…

Accepted Answer

Introduction / Context:This aptitude question tests how to move between list price, cost price, discount percentage and profit or loss percentage. Many competitive exams use this pattern to check whether the candidate can correctly set up equations when both discount and loss or profit are involved. Understanding the relationship between list price, selling price and cost price is essential for solving this kind of profit and loss problem accurately. Given Data / Assumptions: The merchant offers a 30% discount on the list price and then incurs a 16% loss. The same article is sold next time with a 20% discount on the list price. We assume the list price is L and the cost price is CP. We need to find the new profit or loss percentage on cost price when the discount is 20%. Concept / Approach:The key idea is to express everything in terms of cost price and list price. Discount is applied on list price to get the selling price. Profit or loss percentage is always calculated on cost price. First we use the case with 30% discount and 16% loss to link cost price and list price. Then we use this relation to find the new selling price with 20% discount and compute the profit or loss percentage on cost price. Step-by-Step Solution:Step 1: Let the list price be L.Step 2: With 30% discount, selling price SP1 = 0.70 * L.Step 3: At this selling price, there is a 16% loss, so SP1 = 0.84 * CP.Step 4: Therefore 0.70 * L = 0.84 * CP, so CP = (0.70 * L) / 0.84.Step 5: Simplifying, CP = (70/84) * L = (5/6) * L ≈ 0.8333 * L.Step 6: Now consider discount of 20%. New selling price SP2 = 0.80 * L.Step 7: Profit or loss percentage = (SP2 - CP) / CP * 100.Step 8: Substitute CP ≈ 0.8333L and SP2 = 0.80L: (0.80L - 0.8333L) / 0.8333L * 100 ≈ (-0.0333L / 0.8333L) * 100.Step 9: This ratio is approximately -4%, meaning there is a 4% loss on cost price. Verification / Alternative check:We can verify with a convenient numerical value for the list price. Suppose L = 100. Then with 30% discount, selling price is 70. If 70 corresponds to 16% loss, then 70 = 0.84 * CP, giving CP = 70 / 0.84 = 83.33. With 20% discount, selling price becomes 80. The loss is CP - SP2 = 83.33 - 80 = 3.33 on a cost of 83.33, which again gives approximately 4% loss. This numerical check confirms the algebraic calculation and validates the final answer as a loss, not a profit. Why Other Options Are Wrong:Option A (14 percent profit) is incorrect because calculations clearly show the selling price with 20% discount is still below the cost price. Option C (26 percent profit) is much too high and ignores the original loss relationship between list price and cost price. Option D (8 percent profit) also assumes that the new selling price exceeds the cost price, which contradicts the computed values. Only option B correctly describes a 4 percent loss relative to cost price. Common Pitfalls:A common error is to calculate profit or loss directly from the list price or to mix up the base of percentage calculations. Another frequent mistake is to treat both situations independently without first connecting cost price and list price using the given loss condition. Candidates may also mis-handle the negative sign and interpret a negative percentage as profit instead of loss. Careful stepwise handling of equations avoids these issues. Final Answer:The merchant will incur a 4 percent loss when offering a 20% discount on the list price in this situation.

Question 13

Raj sells a machine for Rs 51 lakh at a loss. If instead he had sold the same machine for Rs 60 lakh, his gain would have been eight times his earlier loss. What is the cost price of the machine (in lakh rupees)?

Accepted Answer

Introduction / Context:This question checks understanding of profit and loss when the same article is sold at two different prices, once at a loss and once at a profit. The relationship between these two situations is given in terms of how many times one loss or gain is compared to the other. Such questions are common in aptitude tests to see if the candidate can translate a verbal condition into an algebraic equation involving cost price and selling price. Given Data / Assumptions: First selling price (SP1) is Rs 51 lakh and this sale is at a loss. Second selling price (SP2) is Rs 60 lakh and this sale would be at a profit. The gain at Rs 60 lakh is eight times the loss at Rs 51 lakh. We denote the cost price by CP in lakh rupees. Concept / Approach:Loss is calculated as CP minus SP when CP is greater than SP. Profit is calculated as SP minus CP when SP is greater than CP. The key statement is that the profit at the higher selling price equals eight times the loss at the lower selling price. This gives a simple linear equation in the cost price. Solving this equation yields the unknown cost price of the machine. Step-by-Step Solution:Step 1: Let CP be the cost price in lakhs.Step 2: At SP1 = 51, loss = CP - 51.Step 3: At SP2 = 60, gain = 60 - CP.Step 4: According to the question, gain at Rs 60 lakh is eight times the loss at Rs 51 lakh.Step 5: Therefore, write the equation: 60 - CP = 8 * (CP - 51).Step 6: Expand the right side: 60 - CP = 8CP - 408.Step 7: Bring CP terms to one side: 60 + 408 = 8CP + CP, so 468 = 9CP.Step 8: Thus CP = 468 / 9 = 52.Step 9: So the cost price of the machine is Rs 52 lakh. Verification / Alternative check:We can quickly verify this cost price. If CP is 52, then loss at SP1 (51) is 52 - 51 = 1 lakh. At SP2 (60), profit is 60 - 52 = 8 lakhs. Indeed, the profit of 8 lakhs is exactly eight times the loss of 1 lakh. Thus the condition in the question is satisfied, confirming that the cost price of Rs 52 lakh is correct. Why Other Options Are Wrong:Option A (Rs 59 lakhs) gives loss 8 and gain 1, which does not match the condition that gain be eight times the loss. Option C (Rs 66.375 lakhs) makes SP1 and SP2 both losses, contradicting the statement that there is a gain at Rs 60 lakh. Option D (Rs 45 lakhs) makes both transactions profitable instead of one loss and one gain. Only option B produces the correct ratio of profit to loss as described. Common Pitfalls:Candidates often confuse which expression represents profit and which represents loss, leading to reversed signs in the equation. Another mistake is to apply the eight times relation on absolute selling prices instead of on the monetary gain or loss amount. Also, some students directly set up the equation without checking whether CP is between 51 and 60, which is necessary to have loss in one case and profit in the other. Carefully defining variables before forming the equation avoids these mistakes. Final Answer:The cost price of the machine is Rs 52 lakhs.

Question 14

The marked price of an article is 10% higher than its cost price. If the shopkeeper allows a discount of 10% on the marked price, what happens to the seller with respect to profit or loss on the cost price?

Accepted Answer

Introduction / Context:This question examines a basic profit and loss scenario involving marked price, cost price and discount. It shows that even when a shopkeeper increases the marked price and then gives a discount, the final effect can still be a small loss or profit. This is a classic example to test whether students can correctly handle successive percentage changes on different bases. Given Data / Assumptions: Marked price (MP) is 10% higher than cost price (CP). Discount of 10% is allowed on the marked price. We must determine whether there is profit, loss or no change, and by what percentage on cost price. Assume cost price CP = 100 units for simplicity. Concept / Approach:First raise the cost price by 10% to get the marked price. Then apply a 10% discount on the marked price to get the actual selling price. Note that both percentages are applied on different bases: one on cost price and the other on marked price. Finally, compare the resulting selling price with the original cost price to find the profit or loss percentage. Step-by-Step Solution:Step 1: Let cost price CP = 100.Step 2: Marked price is 10% higher, so MP = 100 + 10% of 100 = 100 + 10 = 110.Step 3: The shopkeeper allows a 10% discount on MP.Step 4: Selling price SP = MP - 10% of MP = 110 - 11 = 99.Step 5: Compare SP with CP. We have CP = 100 and SP = 99.Step 6: Loss = CP - SP = 100 - 99 = 1.Step 7: Loss percentage on cost price = (Loss / CP) * 100 = (1 / 100) * 100 = 1%.Step 8: Therefore the seller incurs a 1% loss. Verification / Alternative check:We can also think in terms of multipliers. Increasing by 10% means multiplying by 1.10. Giving a 10% discount means multiplying by 0.90. So effective factor applied on cost price is 1.10 * 0.90 = 0.99. This means the selling price is 99% of the cost price. Since 99% is 1% less than 100%, this again confirms a 1% loss. This multiplier perspective often simplifies repeated percentage calculations. Why Other Options Are Wrong:Option A (bears no gain, no loss) is wrong because SP is slightly below CP. Option B (gains) is incorrect since CP exceeds SP. Option D (None of these) is not right because one of the specific statements, namely a 1% loss, exactly matches the result. Only option C correctly states that the seller loses 1% on the cost price. Common Pitfalls:Students sometimes wrongly assume that a 10% increase followed by a 10% decrease will cancel out, leading to no gain or loss. This only happens if the percentage changes are applied on the same base, which is not the case here. Another mistake is to apply both percentages on the cost price instead of on cost price and marked price separately. Remember that discount is always calculated on the marked price, not on the cost price. Final Answer:In this transaction, the seller loses 1% on the cost price.

Question 15

By selling cloth at Rs 9 per metre, a shopkeeper incurs a loss of 10% on the cost price. At what price per metre should the cloth be sold so that the shopkeeper earns a profit of 15% on the cost price?

Accepted Answer

Introduction / Context:This question tests the basic connection between cost price, selling price, loss percentage and desired profit percentage. The shopkeeper first sells cloth at a loss, then wants to adjust the selling price to achieve a specific profit. Such questions appear frequently in profit and loss sections of aptitude exams and are straightforward when you correctly derive the cost price first. Given Data / Assumptions: Selling price SP1 = Rs 9 per metre with a loss of 10%. Loss of 10% means SP1 is 90% of cost price. We need a selling price SP2 giving a 15% profit on cost price. All prices refer to one metre of cloth. Concept / Approach:Loss or profit percentage is always calculated on the cost price. First we work backwards from the given selling price and loss percentage to find the cost price per metre. Then we apply the required profit percentage to that cost price to determine the new selling price per metre. This two step process, cost reconstruction followed by target profit calculation, is standard in such problems. Step-by-Step Solution:Step 1: Let cost price per metre be CP.Step 2: Given a 10% loss, we have SP1 = 90% of CP = 0.90 * CP.Step 3: SP1 is Rs 9, so 0.90 * CP = 9.Step 4: Therefore CP = 9 / 0.90 = 10.Step 5: To earn a profit of 15%, selling price SP2 must be 115% of CP.Step 6: SP2 = 1.15 * CP = 1.15 * 10 = 11.5.Step 7: So the required selling price is Rs 11.50 per metre. Verification / Alternative check:If CP is Rs 10 and SP2 is Rs 11.50, then profit per metre is 11.50 - 10 = 1.50 rupees. Profit percentage is (1.50 / 10) * 100 = 15%, which matches the desired rate. Similarly, if SP1 is Rs 9 and CP is Rs 10, then the loss is 10%, which confirms the initial condition. Both checks show the calculations are consistent and the answer is correct. Why Other Options Are Wrong:Option A (Rs 11.20), option B (Rs 11.30) and option C (Rs 11.40) all correspond to smaller profits than 15% when compared with the cost price of Rs 10. For example, Rs 11.20 gives a 12% profit and Rs 11.40 gives a 14% profit. Only option D, Rs 11.50, yields exactly 15% profit, so the other options are not acceptable. Common Pitfalls:Many learners mistakenly take Rs 9 as the cost price, which leads to incorrect calculations of the new selling price. Another common error is mixing up loss and profit percentages, such as adding or subtracting them directly without recalculating based on the cost price. Always reconstruct the cost price from the given loss or profit information before moving to the next step. Final Answer:The cloth should be sold at Rs. 11.50 per metre to earn a 15% profit.

Question 16

A shopkeeper sells almonds at the rate of Rs 1250 per kilogram and at this selling price incurs a loss of 7% on the cost price. If the shopkeeper decides to sell almonds at Rs 1375 per kilogram instead, what will be the result in terms of profit or …

Accepted Answer

Introduction / Context:This problem involves comparing two selling prices for the same commodity and understanding how a change in selling price affects the profit or loss percentage. Here the commodity is almonds sold per kilogram. First the shopkeeper sells at a loss, then increases the selling price and wants to know the new profit or loss percentage. This tests comfort with backward calculation of cost price from a given loss percentage and forward calculation of new profit percentage. Given Data / Assumptions: Initial selling price SP1 = Rs 1250 per kilogram with a 7% loss. New selling price SP2 = Rs 1375 per kilogram. We assume the cost price per kilogram is CP. We have to find the profit or loss percentage when selling at Rs 1375 per kilogram. Concept / Approach:Loss percentage is calculated as (CP - SP) / CP * 100. If we know SP and loss percentage, we can reconstruct CP. Once CP is known, any new selling price can be used to find profit or loss percentage using (SP - CP) / CP * 100. In this question, because the new selling price is slightly above the reconstructed cost price, we expect a small profit instead of a loss. Step-by-Step Solution:Step 1: Let CP be the cost price per kilogram.Step 2: Given that a sale at Rs 1250 causes a 7% loss, we have SP1 = 93% of CP.Step 3: So, 1250 = 0.93 * CP.Step 4: Therefore CP = 1250 / 0.93 ≈ 1344.086.Step 5: Now consider the new selling price SP2 = Rs 1375.Step 6: Profit at SP2 = SP2 - CP ≈ 1375 - 1344.086 ≈ 30.914.Step 7: Profit percentage = (Profit / CP) * 100 ≈ (30.914 / 1344.086) * 100.Step 8: This is approximately 2.3% profit. Verification / Alternative check:We can validate the logic by a quick approximate check. If CP is roughly Rs 1344, then a selling price of Rs 1250 is about Rs 94 below cost. The fraction 94 / 1344 is about 7%, so the loss percentage condition is reasonable. Similarly, Rs 1375 is about Rs 31 above cost, and 31 / 1344 is roughly 2.3%. These quick mental checks confirm that our detailed calculations are on the right track and that the new selling price yields a small profit instead of a loss. Why Other Options Are Wrong:Option A (4.6 percent gain) roughly doubles the true profit percentage and does not match the computation. Option B (2.3 percent loss) has the correct magnitude but the wrong direction, since SP2 is greater than CP and cannot lead to a loss. Option D (4.6 percent loss) is far from the correct result and also wrong in sign. Only option C, a 2.3 percent gain, matches the calculated profit percentage. Common Pitfalls:One common mistake is to assume that a small increase in selling price from 1250 to 1375 automatically converts the 7% loss directly into a large profit, without computing the exact cost price. Another pitfall is forgetting that the loss percentage is based on cost price, not selling price. Students may also round too aggressively and end up choosing a nearby but incorrect option. Accurate use of percentage formulas and careful arithmetic avoid these errors. Final Answer:At the selling price of Rs 1375 per kilogram, the shopkeeper makes a 2.3 percent gain on almonds.

Question 17

If a merchant offers a discount of 4% on the list price of an article, she incurs a loss of 10% on the cost price. What percentage profit or loss will she make if instead she sells the article at a discount of 20% on the list price?

Accepted Answer

Introduction / Context:This problem involves using two different discount scenarios to determine the profit or loss percentage relative to the cost price. The merchant first sells with a small discount and incurs a loss, giving a relationship between list price and cost price. Then the discount is increased, and we must find the new profit or loss percentage. This is a typical question in profit and loss, testing algebraic handling of percentages applied to list price, not directly to cost price. Given Data / Assumptions: Discount of 4% on list price results in a 10% loss on cost price. In the second case, discount is 20% on the same list price. Let list price be L and cost price be CP. We need to compute profit or loss percentage when discount is 20%. Concept / Approach:Discount is always calculated on the list price. Profit or loss percentage, however, is computed on the cost price. First, use the 4% discount and 10% loss to derive the ratio between list price and cost price. Then apply a 20% discount to find the new selling price and compare it with the cost price to compute the new loss percentage. This method ensures that all values are consistent and based on the same cost price. Step-by-Step Solution:Step 1: Let list price be L.Step 2: With 4% discount, selling price SP1 = 0.96 * L.Step 3: At this selling price, there is a 10% loss, so SP1 = 0.90 * CP.Step 4: Therefore 0.96L = 0.90CP, so CP = (0.96 / 0.90) * L = 1.0666... * L.Step 5: Thus CP is greater than L, meaning the list price is actually below the cost price.Step 6: Now consider a 20% discount. New selling price SP2 = 0.80 * L.Step 7: Loss at SP2 = CP - SP2 = (1.0666... * L) - 0.80L = 0.2666... * L.Step 8: Loss percentage = (Loss / CP) * 100 = (0.2666...L / 1.0666...L) * 100 ≈ 25%. Verification / Alternative check:We can set a convenient list price, say L = 100. Then with 4% discount, SP1 = 96. If this is a 10% loss, CP must be 96 / 0.90 ≈ 106.67. With 20% discount, SP2 = 80. Loss at SP2 is 106.67 - 80 = 26.67. Loss percentage is 26.67 / 106.67 ≈ 0.25 or 25%. This numerical confirmation matches the algebraic result and confirms that the second selling situation produces a 25% loss. Why Other Options Are Wrong:Option B (4 percent loss) is too small and would correspond to a selling price close to cost price, which is not the case here. Option C (50 percent profit) and option D (26 percent profit) are impossible because both would require the selling price to be above the cost price, but all calculations show that SP2 is well below CP. Only option A accurately reflects a 25 percent loss. Common Pitfalls:A frequent mistake is to think that increasing the discount by 16 percentage points from 4% to 20% decreases the profit by exactly the same amount, without recalculating correctly based on list price and cost price. Another pitfall is ignoring the given loss condition to derive CP and instead assuming CP equals list price. Always derive CP first when any profit or loss information is provided, then recompute profit or loss under the new selling condition. Final Answer:When the merchant gives a 20% discount on the list price, she makes a 25 percent loss on the cost price.

Question 18

A vendor buys pens at the rate of 4 for Rs 5 and sells them at the rate of 4 for Rs 3. What is the overall result of this transaction in terms of profit or loss percentage?

Accepted Answer

Introduction / Context:This is a classic unit price comparison question. The vendor buys and sells the same item, pens, but at different bulk rates. The aim is to compute the effective cost price and selling price per pen and then determine the gain or loss percentage. Such problems test quick thinking about per unit pricing and profit and loss on that basis. Given Data / Assumptions: Buying rate: 4 pens for Rs 5. Selling rate: 4 pens for Rs 3. The pens are identical and there are no other costs. We need to find overall profit or loss percentage. Concept / Approach:To compare profit or loss accurately, we should convert both bulk rates into single unit rates. The cost price per pen is found by dividing the total cost by the number of pens purchased. The selling price per pen is found by dividing the total selling amount by the number of pens sold. Once we have cost price and selling price per unit, we can calculate profit or loss percentage using the standard formula (SP - CP) / CP * 100. Step-by-Step Solution:Step 1: Compute cost price per pen. If 4 pens cost Rs 5, then CP per pen = 5 / 4 = Rs 1.25.Step 2: Compute selling price per pen. If 4 pens sell for Rs 3, then SP per pen = 3 / 4 = Rs 0.75.Step 3: Find loss per pen: Loss = CP - SP = 1.25 - 0.75 = Rs 0.50.Step 4: Loss percentage = (Loss / CP) * 100 = (0.50 / 1.25) * 100.Step 5: Simplify 0.50 / 1.25 = 1 / 2.5 = 0.4.Step 6: Therefore loss percentage = 0.4 * 100 = 40%.Step 7: So the vendor suffers a 40 percent loss. Verification / Alternative check:We can scale up to a larger common quantity to double check. Suppose the vendor deals with 4 pens. Total cost is Rs 5, total selling revenue is Rs 3. Net loss is Rs 2 on a cost of Rs 5. Loss percentage is (2 / 5) * 100 = 40%, which exactly matches the per pen calculation. This confirms that the earlier steps are correct. Why Other Options Are Wrong:Option A (40 percent gain) uses the correct percentage but with the wrong sign; the vendor clearly loses money. Option B (66.6 percent loss) and option C (66.66 percent gain) are both numerically far from the calculated result. Only option D, 40 percent loss, matches the computed loss percentage and correctly identifies the direction of the transaction outcome. Common Pitfalls:One common mistake is to compare 5 and 3 directly and incorrectly conclude a different percentage without normalizing to a per unit basis. Another is to mistakenly invert CP and SP when applying the formula, leading to a gain percentage instead of a loss. Careful identification of which value is cost and which is selling price and always computing per unit values help avoid these errors. Final Answer:In this transaction the vendor suffers a 40 percent loss.

Question 19

A milkman buys pure milk at Rs 24 per litre and adds one fifth of water to it before selling. He then sells the resulting mixture at Rs 32 per litre. What percentage gain does the milkman make on his cost?

Accepted Answer

Introduction / Context:This question is about profit computation when a trader adulterates a product by adding water, which is assumed to be free. The milkman buys pure milk and adds water to increase the quantity, then sells the mixture at a higher rate per litre. Many aptitude tests include such problems to check understanding of mixtures, unit cost and effective profit percentage when quantity changes but the cost of the added material is zero. Given Data / Assumptions: Cost price of pure milk = Rs 24 per litre. Water is added equal to one fifth of the volume of milk purchased. The mixture is sold at Rs 32 per litre. Water has zero cost. We must find the overall gain percentage on the milkman's cost. Concept / Approach:To solve this, assume a convenient initial quantity of milk, say 1 litre. Compute the total volume of the mixture after adding water. Then work out the total cost, which depends only on the milk part, and the total revenue from selling the entire mixture at the given selling price per litre. Finally, compute profit as revenue minus cost and express profit as a percentage of the cost price. The key idea is that free water increases volume, so effective selling price per litre of milk goes up significantly. Step-by-Step Solution:Step 1: Assume the milkman buys 1 litre of milk. Cost = 1 * 24 = Rs 24.Step 2: He adds one fifth of water. Water added = 1/5 litre.Step 3: Total volume of mixture = 1 + 1/5 = 6/5 litres = 1.2 litres.Step 4: Since water is free, total cost remains Rs 24.Step 5: Selling price per litre of mixture is Rs 32.Step 6: Total revenue from selling 1.2 litres = 1.2 * 32 = Rs 38.4.Step 7: Profit = Revenue - Cost = 38.4 - 24 = Rs 14.4.Step 8: Profit percentage = (Profit / Cost) * 100 = (14.4 / 24) * 100 = 60%. Verification / Alternative check:We can also find effective selling price per litre of pure milk. The milkman sells 1 litre of milk contained in 1.2 litres of mixture for Rs 38.4. Therefore revenue per litre of pure milk is Rs 38.4. Since the cost per litre of pure milk is Rs 24, profit per litre is 38.4 - 24 = 14.4, which again is 60% of 24. This alternate viewpoint confirms the earlier calculation and shows that the milkman gains 60% on his actual money spent. Why Other Options Are Wrong:Option A (50%) and option B (40%) are both less than the computed 60% profit and correspond to smaller revenue or larger assumed cost, which do not match the given numbers. Option C (30%) is even further away and clearly incorrect. Only option D, 60, matches the correctly calculated profit percentage when water is added free of cost and the mixture is sold at Rs 32 per litre. Common Pitfalls:Students sometimes treat the mixture as if it were still one litre and multiply 32 by 1, forgetting that the milkman now sells 1.2 litres. Another common error is assigning cost to water, which changes the profit percentage and makes the answer wrong. Some also incorrectly apply weighted averages without considering that water adds volume but no cost. Careful attention to quantity and cost of each component is essential in mixture and adulteration questions. Final Answer:The milkman makes a 60 percent gain on his cost.

Question 20

A wholesaler sells a box of chocolates at Rs 960 and gains 20% on his cost price. If he decides instead to sell the same box at Rs 1120, what will be his profit percentage?

Accepted Answer

Introduction / Context:This profit and loss question asks you to find a new profit percentage when the selling price changes but the cost price remains the same. The wholesaler initially sells at one price with a known profit percentage and then changes the selling price. The task is to recompute the profit percentage using the unchanged cost and new selling price. These types of questions are very common in aptitude exams and test basic comfort with reverse percentage calculations. Given Data / Assumptions: First selling price SP1 = Rs 960 with 20% profit. Second selling price SP2 = Rs 1120. Cost price CP is the same in both situations. We need to find profit percentage at SP2. Concept / Approach:First reconstruct the cost price from the initial selling price and profit percentage. Profit of 20% means selling price equals 120% of cost price. So CP can be found by dividing SP1 by 1.20. Once CP is known, profit at the new selling price is simply SP2 minus CP. Finally the profit percentage is calculated as (Profit / CP) * 100. This two stage process is standard in profit and loss problems with changed selling price. Step-by-Step Solution:Step 1: Let CP be cost price.Step 2: SP1 = Rs 960 corresponds to a profit of 20%.Step 3: Therefore SP1 = 120% of CP = 1.20 * CP.Step 4: So CP = 960 / 1.20 = Rs 800.Step 5: Now consider the new selling price SP2 = Rs 1120.Step 6: Profit at SP2 = SP2 - CP = 1120 - 800 = Rs 320.Step 7: Profit percentage = (320 / 800) * 100 = 40%.Step 8: Therefore the wholesaler makes 40% profit at the new selling price. Verification / Alternative check:We can check consistency by looking at the ratio of selling price to cost price at SP2. If CP is 800 and SP2 is 1120, then SP2 / CP = 1120 / 800 = 1.4. This means the selling price is 140% of the cost price, which implies a profit of 40%. This ratio check matches the earlier arithmetic and confirms the correctness of the answer. Why Other Options Are Wrong:Option A (30) would imply a selling price of only 130% of cost price, that is 1040 if CP is 800, which does not match the given 1120. Option C (50) would require SP to be 150% of CP or 1200, again not matching. Option D (60) would correspond to 160% of CP or 1280, which is also incorrect. Only option B, 40, matches the profit percentage deduced from the given SP2 of 1120 and CP of 800. Common Pitfalls:Sometimes students mistakenly apply the new profit percentage directly on the original selling price or confuse which base to use for percentage calculation. Another error is to assume the profit increases by the same absolute number of percentage points as the increase in selling price, which is not generally true. Always reconstruct the cost price first when one profit percentage and selling price pair is given, then recompute any new profit or loss percentages from that fixed cost price. Final Answer:At a selling price of Rs 1120, the wholesaler makes a 40 percent profit.

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