Question 1

ITC sells one product at a profit of 20% and another product at a loss of 20%, both at the same selling price. What overall percentage loss does ITC incur on these two products taken together?

Accepted Answer

Introduction / Context:This is a classic misconception question about profit and loss. Many people incorrectly think that a 20% profit on one item and a 20% loss on another item of the same value cancel out. However, when the selling prices or cost prices differ, the percentages do not simply cancel. This problem emphasizes that profit and loss percentages must be considered on the correct base, usually the cost price. Given Data / Assumptions: One product is sold at a profit of 20%. Another product is sold at a loss of 20%. Both products have the same selling price. We need the net percentage loss or gain for ITC on these two products combined. Concept / Approach:Let the common selling price of each product be S. Using the given profit and loss percentages, we can find the cost price for each product. Once the individual cost prices are known, we add them to get total cost and add the selling prices to get total revenue. From there, net profit or loss percentage is computed as (total SP - total CP) / total CP * 100. The key is to recognize that equal percentage profit and loss on different bases do not cancel out. Step-by-Step Solution:Step 1: Let selling price of each product = S.Step 2: For the first product with 20% profit, SP = 1.2 * CP₁ ⇒ CP₁ = S / 1.2.Step 3: For the second product with 20% loss, SP = 0.8 * CP₂ and SP is same S, so S = 0.8 * CP₂ ⇒ CP₂ = S / 0.8.Step 4: Total cost price = CP₁ + CP₂ = S/1.2 + S/0.8.Step 5: Compute: S/1.2 = (5/6)S and S/0.8 = (5/4)S. So total CP = (5/6 + 5/4)S = (10/12 + 15/12)S = (25/12)S.Step 6: Total selling price = S + S = 2S.Step 7: Net loss = total CP - total SP = (25/12)S - 2S = (25/12 - 24/12)S = (1/12)S.Step 8: Loss % = (loss / total CP) * 100 = ((1/12)S) / ((25/12)S) * 100 = (1/25) * 100 = 4%. Verification / Alternative check:To see it numerically, assume S = Rs 120. Then CP₁ = 120 / 1.2 = Rs 100. For the second product, CP₂ = 120 / 0.8 = Rs 150. Total CP = 100 + 150 = Rs 250. Total SP = 120 + 120 = Rs 240. Net loss = 10, and loss% = (10 / 250) * 100 = 4%. This concrete example confirms the algebraic result of 4% loss. Why Other Options Are Wrong:0% is the common misconception that equal gain and loss percentages cancel out. 1% and 2% represent partial miscalculations of the base or mixing the two percentages directly without considering total cost. Only 4% correctly represents the net loss when both transactions are combined using proper cost bases. Common Pitfalls:The biggest pitfall is thinking that profit% and loss% are simple numbers that can be averaged, ignoring that they apply to different cost prices. Another error is taking the average of +20% and -20% as 0% and concluding there is no gain or loss. Always compute total cost and total selling price explicitly when multiple transactions are involved. Final Answer:ITC incurs a net loss of 4% on the two products combined.

Question 2

By selling 17 balls for Rs 720, a shopkeeper incurs a loss equal to the cost price of 5 balls. What is the cost price of one ball?

Accepted Answer

Introduction / Context:This problem links total loss with the cost price of a certain number of items. Instead of giving a direct loss percentage, it states that the total loss is equal to the cost price of 5 balls. From the total selling price and this relation, we can determine the cost price per ball. This type of question trains you to translate verbal loss conditions into algebraic equations. Given Data / Assumptions: Number of balls sold = 17. Total selling price for 17 balls = Rs 720. Total loss is equal to the cost price of 5 balls. We assume all balls have the same cost price. We must find cost price per ball. Concept / Approach:Let cost price of one ball be c. Then total cost price for 17 balls is 17c. Let total loss be L. The selling price is total cost - loss, i.e., SP = 17c - L. Given that L equals the cost of 5 balls, L = 5c. So SP = 17c - 5c = 12c. Setting this equal to 720 allows us to solve for c. This approach converts a word relation between loss and cost into a simple linear equation. Step-by-Step Solution:Step 1: Let cost price per ball = c.Step 2: Cost price of 17 balls = 17c.Step 3: Loss is equal to cost of 5 balls, so loss L = 5c.Step 4: Selling price of 17 balls SP = total CP - loss = 17c - 5c = 12c.Step 5: Given SP = Rs 720, so 12c = 720 ⇒ c = 720 / 12 = Rs 60. Verification / Alternative check:With c = Rs 60, total cost of 17 balls = 17 * 60 = Rs 1,020. Total loss is cost of 5 balls = 5 * 60 = Rs 300. Therefore, actual selling price = cost - loss = 1,020 - 300 = Rs 720, which matches the given selling price. This confirms that the cost price per ball is correctly found as Rs 60. Why Other Options Are Wrong:Rs 55, Rs 65 and Rs 70 do not satisfy the given relationship when used in the same equations. For example, if cost were Rs 55, total cost for 17 balls would be Rs 935 and losing 5 * 55 = Rs 275 would lead to SP = Rs 660, not Rs 720. Similar contradictions appear for Rs 65 and Rs 70. Only Rs 60 produces the correct total selling price of Rs 720 when the loss equals the cost of 5 balls. Common Pitfalls:Some students incorrectly assume that the loss equals 5/17 of the selling price instead of 5 times the cost price of one ball. Others try to compute a loss percentage first, which is unnecessary. The simplest method is to use a variable for cost price, set up the equation using the relation between loss and cost, and then solve directly for that variable. Final Answer:The cost price of each ball is Rs. 60.

Question 3

A merchant buys two articles together for Rs 600. He sells one article at a profit of 22% and the other at a loss of 8%, and overall he makes no profit and no loss. What is the selling price of the article that he sells at a loss?

Accepted Answer

Introduction / Context:This question is a typical example of mixed transactions where one item is sold at profit and another at loss, but the overall result is break-even. To solve it, we must split the total cost into two unknown cost prices, apply the respective profit and loss percentages, and use the condition that overall profit is zero. From there, we can determine the selling price of the loss-making article. Given Data / Assumptions: Total cost price of two articles = Rs 600. First article is sold at a profit of 22%. Second article is sold at a loss of 8%. Net result: no profit and no loss overall. We need the selling price of the article sold at a loss. Concept / Approach:Let cost price of the profit article be x and cost price of the loss article be 600 - x. Using the profit and loss percentages, we express both selling prices in terms of x. The condition of no overall profit means total selling price equals total cost price (600). This gives a linear equation in x. Solving for x gives both cost prices, from which we can compute the selling price of the loss article as 92% of its cost price. Step-by-Step Solution:Step 1: Let cost of article 1 (profit article) = x.Step 2: Then cost of article 2 (loss article) = 600 - x.Step 3: Selling price of article 1, SP₁ = x * 1.22.Step 4: Selling price of article 2, SP₂ = (600 - x) * 0.92.Step 5: No profit, no loss implies SP₁ + SP₂ = 600.Step 6: So 1.22x + 0.92(600 - x) = 600 ⇒ 1.22x + 552 - 0.92x = 600 ⇒ 0.30x = 48 ⇒ x = 160.Step 7: Then cost of loss article = 600 - 160 = 440, and SP₂ = 0.92 * 440 = 404.8. Verification / Alternative check:Check with the computed values: Article 1 has CP = 160 and SP = 160 * 1.22 = 195.2 (profit 35.2). Article 2 has CP = 440 and SP = 404.8 (loss 35.2). Total CP = 600 and total SP = 195.2 + 404.8 = 600. Since the total profit is zero, our solution is consistent and confirms that SP of the loss article is Rs 404.80. Why Other Options Are Wrong:Rs 536.80 and Rs 440 do not satisfy the zero net profit condition when used as SP for the loss article. Rs 160 is only the cost price of the profit article, not a selling price at all. Only Rs 404.80 correctly balances the gain on one article with the loss on the other so that the merchant neither gains nor loses overall. Common Pitfalls:Students often assume that the two cost prices are equal or that the profit and loss percentages somehow cancel out symmetrically. Others forget to apply percentages to the correct base and mix up profit and loss formulas. Always introduce variables for unknown cost prices, translate the conditions into equations and then solve systematically. Final Answer:The selling price of the article sold at a loss is Rs. 404.80.

Question 4

A shopkeeper X sells fruits at a profit of 21%. If X had bought the fruits for 9% less and sold them for Rs 29 less, he would have earned a profit of 25%. What is the original cost price of the fruits?

Accepted Answer

Introduction / Context:This is a layered percentage problem involving two hypothetical scenarios. X sells fruits at 21% profit in the original case. In an imaginary second case, both cost price and selling price are changed, and the profit becomes 25%. By comparing the two situations, we can determine the original cost price. This type of question tests your ability to form and solve equations with percentage changes applied to both cost and selling prices. Given Data / Assumptions: Original profit = 21%. If fruits had been bought 9% cheaper, the new cost price would be 91% of original cost price. In the hypothetical case, fruits are sold for Rs 29 less than original selling price. Under that scenario, profit would be 25%. We need to find the original cost price. Concept / Approach:Let original cost price be C. Then original selling price is SP₁ = 1.21C. In the second scenario, new cost price is 0.91C and new selling price is SP₂ = SP₁ - 29. We are told that SP₂ gives 25% profit on 0.91C, so SP₂ = 1.25 * 0.91C. Equating these two expressions for SP₂ gives an equation in C, which we can solve to obtain the original cost price. This structured algebraic approach avoids confusion between the two different profit rates. Step-by-Step Solution:Step 1: Let original cost price = C.Step 2: Original selling price SP₁ = 1.21C (because profit is 21%).Step 3: If fruits were bought 9% cheaper, new cost price = 0.91C.Step 4: In the second case, selling price is SP₂ = SP₁ - 29 = 1.21C - 29.Step 5: Given that SP₂ gives 25% profit on 0.91C, so SP₂ = 1.25 * 0.91C = 1.1375C.Step 6: Equate the two expressions: 1.21C - 29 = 1.1375C.Step 7: 1.21C - 1.1375C = 29 ⇒ 0.0725C = 29 ⇒ C = 29 / 0.0725 = 400. Verification / Alternative check:Using C = 400, original SP₁ = 1.21 * 400 = Rs 484. New cost price = 0.91 * 400 = Rs 364. New SP₂ = SP₁ - 29 = 484 - 29 = Rs 455. The profit in this second case is 455 - 364 = Rs 91. Profit percentage = (91 / 364) * 100 = 25%. This matches the condition that the second scenario yields a 25% profit, confirming that the original cost price must be Rs 400. Why Other Options Are Wrong:If the cost price were Rs 420, 460 or 480, the relationship between selling prices and profit percentages would not match the described conditions. For instance, plugging in 420 would not give the second profit exactly 25% when both the cost and selling price are adjusted as described. Only C = 400 satisfies both the original 21% profit and the modified 25% profit scenario simultaneously. Common Pitfalls:Common mistakes include subtracting 9% from the 21% profit directly, or trying to average percentages, which is incorrect here. Another error is forgetting that the Rs 29 difference applies to the selling price, not to the profit. The safest strategy is to always introduce a variable for cost price, write explicit expressions for all relevant selling prices and then carefully equate them using the conditions provided. Final Answer:The original cost price of the fruits is Rs. 400.

Question 5

A trader buys an item for Rs 30 and sells it for Rs 50. What is his profit percentage on this transaction?

Accepted Answer

Introduction / Context:This is a straightforward profit percentage question where both cost price and selling price are explicitly given. Such questions verify whether you remember the correct formula for profit% and can apply it accurately without mixing up the numerator and denominator. Even though the numbers are simple, careless mistakes are common in timed exams. Given Data / Assumptions: Cost price (CP) of the item = Rs 30. Selling price (SP) of the item = Rs 50. There are no additional costs or taxes. We must find the percentage profit earned by the trader. Concept / Approach:Profit is defined as the difference between selling price and cost price. Profit percentage is always calculated on the cost price unless stated otherwise. The formula is: profit% = (SP - CP) / CP * 100. Once the profit amount is known, we simply divide by CP and convert to a percentage. This basic ratio concept is fundamental to all profit and loss questions. Step-by-Step Solution:Step 1: Identify CP = 30 and SP = 50.Step 2: Compute profit = SP - CP = 50 - 30 = 20.Step 3: Use the formula profit% = (profit / CP) * 100.Step 4: Profit% = (20 / 30) * 100.Step 5: 20 / 30 = 2 / 3 ≈ 0.6667, so profit% ≈ 66.67%. Verification / Alternative check:If the trader gains 66.67% on a cost price of Rs 30, the selling price should be CP * (1 + 66.67/100) = 30 * (1 + 2/3) = 30 * 5/3 = 50. This matches the actual selling price, confirming that the computed profit percentage is correct. Any other percentage would not convert back to the exact selling price of Rs 50 when multiplied with the cost price. Why Other Options Are Wrong:40%, 45% and 35% all represent profit amounts that are too small for an increase from Rs 30 to Rs 50. For example, a 40% profit would correspond to a selling price of 30 * 1.4 = 42, not 50. The difference between SP and CP here is quite large relative to the base, so the correct percentage must also be relatively large, which is captured by 66.67% and not by the smaller options. Common Pitfalls:A common mistake is to divide the profit by the selling price instead of the cost price or to incorrectly compute 20/30 as 20/50. Another pitfall is to misinterpret the percentage as 50/30 * 100. Always remember that profit percentage is based on cost price, and carefully place values into the formula to avoid such arithmetic errors. Final Answer:The trader earns a profit of approximately 66.67% on the item.

Question 6

A college bag is sold for Rs 1,540. The cost price of the bag is 240% more than the profit obtained on it at this selling price. What is the cost price of the college bag?

Accepted Answer

Introduction / Context:This profit and loss question expresses the relationship between cost price and profit using a percentage comparison, rather than giving a direct profit percentage. The cost price is said to be 240% more than the profit amount. From the selling price and this relationship, we must find the cost price. Problems like this test your ability to convert percentage comparisons between profit and cost into algebraic equations. Given Data / Assumptions: Selling price (SP) of the college bag = Rs 1,540. Cost price (CP) is 240% more than the profit. If profit is P, then CP = P + 240% of P. We assume no extra charges or hidden costs. We need to determine CP. Concept / Approach:Let the profit be P. Saying that the cost price is 240% more than the profit means CP = P + 2.4P = 3.4P. Since selling price equals cost price plus profit, SP = CP + P. Substituting CP = 3.4P into SP = CP + P gives SP = 4.4P. With a known SP of 1,540, we can solve for P and then find CP. This method is a straightforward application of algebra and percentage increase relationships. Step-by-Step Solution:Step 1: Let profit = P.Step 2: Cost price is 240% more than profit, so CP = P + 2.4P = 3.4P.Step 3: Selling price SP = CP + P = 3.4P + P = 4.4P.Step 4: Given SP = 1,540, so 4.4P = 1,540.Step 5: P = 1,540 / 4.4 = 350.Step 6: Therefore CP = 3.4P = 3.4 * 350 = 1,190. Verification / Alternative check:Consider CP = Rs 1,190 and profit = Rs 350. The statement says that CP is 240% more than profit. Check: 240% of 350 = 2.4 * 350 = 840. Then profit plus this extra 240% is 350 + 840 = 1,190, which matches CP. Also, SP = CP + profit = 1,190 + 350 = 1,540, exactly the given selling price. Both conditions are satisfied, confirming our calculation. Why Other Options Are Wrong:Other values such as Rs 1,288, Rs 1,365 and Rs 1,452 do not simultaneously satisfy SP = CP + profit and the ratio CP = P + 240% of P when you solve for profit. Plugging them into the relationships leads to contradictions. Only Rs 1,190 fits both the given selling price and the specified percentage relationship between cost price and profit. Common Pitfalls:Many students misread “240% more than the profit” as “240% of the profit” and set CP = 2.4P instead of 3.4P. Others mistakenly try to interpret 240% as a profit percentage on cost price. Always read such statements carefully, distinguishing between “is 240% of” and “is 240% more than,” as they mean different things mathematically. Final Answer:The cost price of the college bag is Rs. 1190.

Question 7

An article is sold for Rs 753, and the profit earned is equal to the loss incurred when the same article is sold for Rs 455. At what price should the article be sold to obtain a profit of 50%?

Accepted Answer

Introduction / Context:This question uses a symmetry condition between profit and loss at two different selling prices. The profit when selling at Rs 753 equals the loss when selling at Rs 455. From this, we can deduce the cost price. Once the cost price is known, we can easily compute the selling price required for a desired profit of 50%. This style of problem is common in exams and tests your algebraic setup skills. Given Data / Assumptions: First selling price SP₁ = Rs 753 (profit case). Second selling price SP₂ = Rs 455 (loss case). Profit at SP₁ is equal to loss at SP₂. We need selling price for a 50% profit. Cost price (CP) is the same in all cases. Concept / Approach:If CP is C, profit at SP₁ is (753 - C), and loss at SP₂ is (C - 455). These two are given equal, so 753 - C = C - 455. This equation allows us to solve for C. Then to get 50% profit, new selling price SP₃ must be 1.5 times CP, because 50% profit means adding half of cost price to cost. This two-step approach is reliable and direct. Step-by-Step Solution:Step 1: Let cost price = C.Step 2: Profit at SP₁ = 753 - C.Step 3: Loss at SP₂ = C - 455.Step 4: Given that profit equals loss, so 753 - C = C - 455.Step 5: Rearranging, 753 + 455 = 2C ⇒ 1,208 = 2C ⇒ C = 604.Step 6: For a 50% profit, SP₃ = C * 1.5 = 604 * 1.5 = 906. Verification / Alternative check:Check the equality condition using C = 604. Profit at Rs 753 is 753 - 604 = 149. Loss at Rs 455 is 604 - 455 = 149. They are equal, satisfying the main condition. For a 50% profit, profit amount should be 0.5 * 604 = 302, giving SP₃ = 604 + 302 = 906, which matches our computed selling price and confirms correctness. Why Other Options Are Wrong:Rs 855, Rs 955 and Rs 896 correspond to profit percentages that are not exactly 50% when applied to a cost price of Rs 604. For example, 855 gives profit of 855 - 604 = 251, which is about 41.56%, not 50%. Only Rs 906 yields precisely 50% profit relative to the cost price found from the equal profit and loss condition. Common Pitfalls:Sometimes students add or subtract the two selling prices directly without forming equations or mistakenly think that the cost price is the average of the two selling prices. While in this particular case C does turn out to be the average, that result follows from correctly setting 753 - C = C - 455, not from an unsupported shortcut. Always derive such relationships from first principles to avoid errors in less symmetric cases. Final Answer:To earn a 50% profit, the article should be sold for Rs. 906.

Question 8

John buys a laptop for Rs 1,75,000 and sells it to Mark at a loss of 20%. Mark then sells it to Kevin at a profit of 25%. Kevin later returns the laptop to Mark but can recover only Rs 4.50 for every Rs 5 he had paid. What is the amount of loss incu…

Accepted Answer

Introduction / Context:This is a chain transaction problem involving successive buying and selling between three people: John, Mark and Kevin. Each transaction has its own profit or loss condition. Finally, Kevin returns the laptop and recovers only a fraction of what he paid. We must track Kevin's outflow and inflow of money to determine his net loss. Problems of this type test careful step-by-step tracking of multiple profit and loss operations. Given Data / Assumptions: John's cost price = Rs 1,75,000. John sells to Mark at a loss of 20%. Mark sells to Kevin at a profit of 25%. When Kevin returns the laptop, he receives only Rs 4.50 for every Rs 5 he originally paid. We must find Kevin's monetary loss. Concept / Approach:We first compute the price at which John sells to Mark using the 20% loss. Then we compute the price at which Mark sells to Kevin using the 25% profit on Mark's cost. That price is Kevin's purchase price. When Kevin returns the laptop, he gets 4.5/5 of what he paid. His loss is the difference between what he paid and what he recovered. Each step uses profit or loss percentage formula SP = CP * (1 ± rate). Step-by-Step Solution:Step 1: John's cost price = Rs 1,75,000.Step 2: John sells to Mark at 20% loss, so Mark's cost price = 1,75,000 * 0.8 = Rs 1,40,000.Step 3: Mark sells to Kevin at 25% profit, so Kevin's buying price = 1,40,000 * 1.25 = Rs 1,75,000.Step 4: When Kevin returns the laptop, he recovers only Rs 4.50 for every Rs 5 he paid, i.e., 4.5/5 = 0.9 of his purchase price.Step 5: Amount Kevin recovers = 0.9 * 1,75,000 = Rs 1,57,500.Step 6: Kevin's loss = amount paid - amount recovered = 1,75,000 - 1,57,500 = Rs 17,500. Verification / Alternative check:Notice that Kevin originally pays Rs 1,75,000 and effectively gets back 90% of this amount, since 4.5/5 equals 0.9. Losing 10% of 1,75,000 gives 0.1 * 1,75,000 = 17,500, which matches the detailed calculation above. The intermediate Mark transaction is important for understanding how Kevin's purchase price arises, but once it is known, Kevin's loss is simply 10% of that amount. Why Other Options Are Wrong:Rs 16,500, Rs 14,200 and Rs 15,520 are values that might appear if one misapplies the profit and loss percentages at different stages, or if one mistakenly calculates 10% on the wrong base such as John's cost price or Mark's cost price. Only Rs 17,500 correctly represents 10% of Kevin's actual purchase price of Rs 1,75,000, given the 4.5 to 5 repayment ratio. Common Pitfalls:A frequent mistake is to think that Mark's profit or John's loss somehow affects Kevin's eventual percentage loss directly. In reality, Kevin's loss depends only on what he paid and what he recovered. Another pitfall is to confuse the 4.5 to 5 ratio with a 5% loss instead of a 10% loss. Always convert the ratio to a decimal and compare it with 1 to find the correct percentage change. Final Answer:Kevin incurs a loss of Rs. 17,500 on the laptop transaction.

Question 9

Labour cost is 20% of the cost of production and raw material cost is 10% of the cost of production. The selling price is 20% above the cost of production. If labour cost increases by 40% and raw material cost increases by 20%, while other expenses …

Accepted Answer

Introduction / Context:This question involves cost structure analysis where different components of total cost change by different percentages. Labour and raw materials are specified as percentages of the original cost of production, and then both are increased. The selling price is also changed. We must recompute the total cost and the new selling price, then calculate the resulting profit percentage. This kind of question is common in business math and managerial aptitude tests. Given Data / Assumptions: Original total cost of production = C (assumed). Original labour cost = 20% of C = 0.2C. Original raw material cost = 10% of C = 0.1C. Other expenses = 70% of C = 0.7C. Original selling price SP₁ = 20% above cost = 1.2C. Labour cost increases by 40% and raw material cost by 20%. Other expenses remain at 0.7C. New selling price SP₂ is 10% higher than SP₁. Concept / Approach:We first compute the new cost components after the increases. The new labour cost becomes 1.4 times the old labour cost, and the new raw material cost becomes 1.2 times the old raw material cost. Adding these to the unchanged other expenses gives a new total cost. The selling price is raised by 10% over the original selling price. Finally, profit% is computed as (SP₂ - new cost) / new cost * 100. Because we use C as a symbolic base, we do not need its actual numeric value. Step-by-Step Solution:Step 1: Original cost C is broken down as: labour = 0.2C, raw material = 0.1C, others = 0.7C.Step 2: Original selling price SP₁ = 1.2C.Step 3: Labour cost increases by 40%, so new labour cost = 0.2C * 1.4 = 0.28C.Step 4: Raw material cost increases by 20%, so new raw material cost = 0.1C * 1.2 = 0.12C.Step 5: Other expenses remain unchanged at 0.7C.Step 6: New total cost C₂ = 0.28C + 0.12C + 0.7C = 1.1C.Step 7: Selling price is increased by 10% over SP₁, so SP₂ = 1.1 * SP₁ = 1.1 * 1.2C = 1.32C.Step 8: New profit = SP₂ - C₂ = 1.32C - 1.1C = 0.22C.Step 9: New profit percentage = (0.22C / 1.1C) * 100 = 0.2 * 100 = 20%. Verification / Alternative check:Take a simple numerical value, such as C = 100. Then original costs are labour = 20, raw = 10, others = 70, SP₁ = 120. After the changes, new labour cost = 28, new raw cost = 12, others = 70, so new total cost C₂ = 110. New selling price SP₂ = 1.1 * 120 = 132. Profit = 132 - 110 = 22, and profit% = (22 / 110) * 100 = 20%. This numeric example confirms our symbolic result. Why Other Options Are Wrong:Profit percentages like 18%, 22% or 24% arise if one incorrectly adjusts only some components of cost or wrongly applies the 10% increase directly to cost instead of selling price. The only value that properly balances the increased cost elements with the higher selling price is 20%. Common Pitfalls:Some common mistakes include adding percentage increases directly (for example, adding 40% and 20% and 10%) without considering their different bases, or misinterpreting “20% of cost of production” for labour and raw material share. Another error is to recompute selling price as 20% plus 10% above cost instead of 10% above the old selling price. Keeping careful track of which percentage applies to which base is essential in multi-step cost structure questions. Final Answer:After all changes, the new profit percentage for the industry is 20%.

Question 10

An item is sold at a loss of 10%. Had it been sold for Rs 9 more, there would have been a profit of 25/2% (that is, 12.5%). What is the cost price of the item?

Accepted Answer

Introduction / Context:This is a standard profit and loss question where the item is sold at a loss in one scenario, and a slightly higher selling price would convert the loss into a profit. By comparing the two situations, we can set up an equation in terms of the cost price. Such questions test your ability to apply profit and loss formulas in two different cases for the same cost price. Given Data / Assumptions: In the first case, the item is sold at a loss of 10%. If sold for Rs 9 more than the first selling price, there would be a profit of 25/2% = 12.5%. Cost price (CP) is the same in both cases. We must find the cost price of the item. Concept / Approach:If CP is C, then a 10% loss implies first selling price SP₁ = 0.9C. The second selling price is SP₂ = SP₁ + 9. We are also told that SP₂ corresponds to a 12.5% profit, so SP₂ = 1.125C. Equating these two expressions for SP₂ gives us a simple linear equation in C. Solving this equation yields the cost price. Step-by-Step Solution:Step 1: Let cost price = C.Step 2: At 10% loss, first selling price SP₁ = 0.9C.Step 3: Second selling price SP₂ = SP₁ + 9 = 0.9C + 9.Step 4: Second case has 12.5% profit, so SP₂ = 1.125C.Step 5: Equate them: 0.9C + 9 = 1.125C.Step 6: 9 = 1.125C - 0.9C = 0.225C ⇒ C = 9 / 0.225 = 40. Verification / Alternative check:Check with CP = Rs 40. At 10% loss, SP₁ = 0.9 * 40 = Rs 36. If sold for Rs 9 more, second selling price is SP₂ = 36 + 9 = Rs 45. Profit at SP₂ is 45 - 40 = Rs 5. Profit% = (5 / 40) * 100 = 12.5%, which equals 25/2%. This confirms that CP = Rs 40 fits both conditions exactly. Why Other Options Are Wrong:CP values like Rs 90, Rs 75 and Rs 55 do not yield a difference of exactly Rs 9 between the loss-making selling price and the profit-making selling price while also matching the specified percentages. For example, with CP = 90, 10% loss gives SP₁ = 81, and a 12.5% profit gives SP₂ = 101.25, whose difference is 20.25, not 9. Hence they are incorrect. Common Pitfalls:Some learners misread 25/2% as 25% or mistakenly consider the Rs 9 as a change in cost price instead of selling price. Another error is to attempt to find profit or loss percentages using arbitrary assumptions rather than forming a precise equation. Always translate both scenarios into algebraic expressions involving CP and then solve systematically. Final Answer:The cost price of the item is Rs. 40.

Question 11

In an exhibition, Almond buys a painting for Rs 20,000 and sells it to Olive for Rs 23,000. Olive then sells it to Sarah at double Almond's profit percentage. At what price should Sarah sell this painting to earn a profit of 8%?

Accepted Answer

Introduction / Context:This is another chain transaction problem where the painting changes hands three times. Almond earns one profit percentage, Olive earns double that percentage, and finally Sarah wants to earn 8% profit on her purchase. The question requires us to track cost prices and selling prices step by step to find Sarah's required selling price. It tests careful use of percentage profit at different stages. Given Data / Assumptions: Almond buys the painting for Rs 20,000. He sells it to Olive for Rs 23,000. Olive's profit percentage is double Almond's profit percentage. Sarah buys the painting from Olive at Olive's selling price. Sarah wants to earn 8% profit on her own cost price. We need Sarah's selling price that gives her 8% profit. Concept / Approach:First, determine Almond's profit percentage using his cost and selling price. Then double this percentage to get Olive's profit percentage. Use Olive's percentage to compute her selling price to Sarah and confirm that it matches the given information. This selling price is Sarah's cost price. Finally, apply 8% profit on Sarah's cost price to find the price at which she must sell the painting. Each step uses the formula SP = CP * (1 + profit%). Step-by-Step Solution:Step 1: Almond's cost price = Rs 20,000, selling price to Olive = Rs 23,000.Step 2: Almond's profit = 23,000 - 20,000 = Rs 3,000.Step 3: Almond's profit percentage = (3,000 / 20,000) * 100 = 15%.Step 4: Olive's profit percentage is double Almond's, so Olive's profit% = 30%.Step 5: Olive bought the painting for Rs 23,000, so she sells it to Sarah at SP = 23,000 * 1.30 = Rs 29,900 (this is Sarah's cost price).Step 6: Sarah wants an 8% profit, so her selling price must be SP_Sarah = 29,900 * 1.08 = Rs 32,292. Verification / Alternative check:Check Sarah's profit: Profit = 32,292 - 29,900 = Rs 2,392. Profit% = (2,392 / 29,900) * 100 ≈ 8%. This confirms that Rs 32,292 is the correct selling price for Sarah to achieve an 8% profit. The earlier steps also align: Olive earns 30% profit on 23,000, giving 23,000 * 1.30 = 29,900, so all transaction stages are consistent. Why Other Options Are Wrong:Other values like Rs 34,410, Rs 31,184 and Rs 29,999 correspond to profit percentages different from 8%. For instance, selling at Rs 34,410 would give Sarah a much higher profit than 8%, while Rs 29,999 might give little or no profit. Only Rs 32,292 results in exactly 8% profit over her cost price of Rs 29,900. Common Pitfalls:Some learners might mistakenly double Almond's profit amount instead of his profit percentage for Olive, or they may treat Olive's selling price as 23,000 + 3,000 rather than 30% of 23,000. Another frequent error is to apply Sarah's 8% on the original 20,000 instead of on her actual purchase price from Olive. Always apply each profit percentage to the correct individual cost price at that stage of the transaction chain. Final Answer:Sarah should sell the painting for Rs. 32,292 to earn an 8% profit.

Question 12

A shopkeeper sells a mobile phone for Rs 12,000. Had he offered a discount of 10% on this selling price, he would have incurred a loss of 4%. What is the cost price of the mobile phone?

Accepted Answer

Introduction / Context:This question mixes a given selling price with a hypothetical discounted selling price that would result in a loss. By working backward from the hypothetical case, we can determine the cost price. This structure is common in exam problems, where you must convert a worded condition about possible discounts and losses into clear algebraic steps. Given Data / Assumptions: Actual selling price of the mobile phone SP₁ = Rs 12,000. If a discount of 10% had been offered on this price, the phone would have been sold at SP₂ = 90% of 12,000. At SP₂, the shopkeeper would have incurred a loss of 4%. Cost price (CP) is the same in both scenarios. We must find the cost price of the phone. Concept / Approach:A 10% discount on the given selling price means the hypothetical selling price SP₂ is 0.9 * 12,000. At that price, the shopkeeper loses 4%, so SP₂ equals 96% of CP, or SP₂ = 0.96 * CP. This equation allows us to solve for CP. Once CP is known, we can confirm that selling at 12,000 would indeed yield a profit rather than a loss, consistent with the scenario. Step-by-Step Solution:Step 1: Actual selling price SP₁ = 12,000.Step 2: If a 10% discount were given, hypothetical selling price SP₂ = 0.9 * 12,000 = Rs 10,800.Step 3: At SP₂, there would be a loss of 4%, so SP₂ = 0.96 * CP.Step 4: Therefore, 10,800 = 0.96 * CP.Step 5: CP = 10,800 / 0.96 = Rs 11,250. Verification / Alternative check:With CP = 11,250, selling at SP₂ = 10,800 gives loss = 11,250 - 10,800 = 450. Loss% = (450 / 11,250) * 100 = 4%. Selling at the original price of 12,000 gives profit = 12,000 - 11,250 = 750. Profit% = (750 / 11,250) * 100 ≈ 6.67%. Both percentages match the intended conditions, confirming that the cost price is Rs 11,250. Why Other Options Are Wrong:Cost price values like Rs 12,500, Rs 12,750 and Rs 11,680 do not yield a 4% loss at the discounted price of Rs 10,800. For example, if CP were 12,500, loss at 10,800 would be 1,700, giving a loss percentage of 13.6%, not 4%. Only Rs 11,250 fits the equation 10,800 = 0.96 * CP and the resulting percentages correctly. Common Pitfalls:Students sometimes apply the 10% discount to cost price instead of the given selling price, or they treat the 4% loss as being on the selling price. Another error is to think that the 10% and 4% can be combined or averaged. Always apply each percentage to its proper base: discount on selling price or marked price, and loss percentage on cost price. Final Answer:The cost price of the mobile phone is Rs. 11,250.

Question 13

A merchant buys two items together for Rs 7,500. He sells one item at a profit of 16% and the other item at a loss of 14%. Overall he makes no profit and no loss. What is the difference between the selling prices of the two items?

Accepted Answer

Introduction / Context:This final question is similar in structure to an earlier one: two items are bought together, one sold at profit and the other at loss, with a net result of no overall gain or loss. Here, instead of asking for a particular selling price, the problem asks for the difference between selling prices. This tests your ability to set up equations with multiple unknowns and then compute a derived quantity (difference) rather than a direct variable. Given Data / Assumptions: Total cost price of the two items = Rs 7,500. First item is sold at 16% profit. Second item is sold at 14% loss. Net effect: no profit, no loss. We must find the difference between the selling prices of the two items. Concept / Approach:Let cost price of the profit item be x and cost price of the loss item be 7,500 - x. The corresponding selling prices are 1.16x and 0.86(7,500 - x). The condition of zero net profit implies total selling price equals total cost, so 1.16x + 0.86(7,500 - x) = 7,500. Solving this equation gives x, and thus the two selling prices. The absolute difference between these two selling prices is then our required answer. Step-by-Step Solution:Step 1: Let cost price of item 1 (profit item) = x.Step 2: Cost price of item 2 (loss item) = 7,500 - x.Step 3: Selling price of item 1, SP₁ = 1.16x.Step 4: Selling price of item 2, SP₂ = 0.86(7,500 - x).Step 5: No overall profit means SP₁ + SP₂ = 7,500.Step 6: So 1.16x + 0.86(7,500 - x) = 7,500.Step 7: Expand: 1.16x + 6,450 - 0.86x = 7,500 ⇒ (1.16x - 0.86x) + 6,450 = 7,500.Step 8: 0.30x = 1,050 ⇒ x = 1,050 / 0.30 = 3,500.Step 9: Then SP₁ = 1.16 * 3,500 = 4,060 and SP₂ = 0.86 * (7,500 - 3,500) = 0.86 * 4,000 = 3,440.Step 10: Difference in selling prices = |4,060 - 3,440| = Rs 620. Verification / Alternative check:Check that net profit is indeed zero. Total cost = 7,500. Total selling price = 4,060 + 3,440 = 7,500. Since total SP equals total CP, the merchant neither gains nor loses overall. The difference of Rs 620 is purely the result of the different profit and loss percentages applied to different cost price portions, confirming our calculation. Why Other Options Are Wrong:Values such as Rs 654, Rs 725 and Rs 747 would appear only if one mis-specified the profit or loss percentages, or incorrectly apportioned the total cost between the two items. They do not maintain the required condition of zero net profit when recomputing total selling price. Only Rs 620 fits all given information. Common Pitfalls:Some students assume equal cost prices for both items or attempt to average profit and loss percentages. Others forget that the net result being zero profit means total selling price must equal total cost. Always define variables for the unknown cost prices, correctly express selling prices in terms of those variables, and use the net profit condition to derive your equations. Final Answer:The difference between the selling prices of the two items is Rs. 620.

Question 14

A quantity of tea is sold at Rs. 5.75 per kilogram and the total profit on the sale is Rs. 60. If the trader makes a profit of exactly 15 percent on the deal, what is the total quantity of tea (in kilograms) that is sold?

Accepted Answer

Introduction / Context: This aptitude question checks the basic concepts of profit and loss, especially how to relate the selling price per kilogram, cost price per kilogram, total profit, and total quantity sold. Such questions are common in banking exams, SSC exams, and other competitive tests that include quantitative aptitude sections. Given Data / Assumptions: Selling price per kilogram of tea (SP) = Rs. 5.75 Profit percentage on cost price = 15 percent Total profit earned on the transaction = Rs. 60 We assume all tea is sold at the same rate without any wastage. Concept / Approach: The key idea is that profit is the difference between selling price and cost price multiplied by the quantity. When we know the profit percentage and selling price per kilogram, we can compute the cost price per kilogram. Once the per kilogram profit is known, dividing the total profit by profit per kilogram gives the total quantity of tea sold. Step-by-Step Solution: Let cost price per kilogram be CP. Given profit percent = 15 percent, so SP = CP * (1 + 15 / 100). Therefore SP = CP * 1.15. We know SP = 5.75, so 5.75 = 1.15 * CP. Thus CP = 5.75 / 1.15 = 5 rupees per kilogram. Profit per kilogram = SP - CP = 5.75 - 5.00 = 0.75 rupees per kilogram. Total profit = profit per kilogram * quantity. 60 = 0.75 * quantity. Quantity = 60 / 0.75 = 80 kilograms. Verification / Alternative check: If quantity is 80 kg, total cost = 80 * 5 = Rs. 400. Total selling price = 80 * 5.75 = Rs. 460. Profit = 460 - 400 = Rs. 60, which matches the given profit. The computed quantity is therefore consistent with the given information. Why Other Options Are Wrong: 72 kg: Profit would be 72 * 0.75 = Rs. 54, which is less than Rs. 60. 76 kg: Profit would be 76 * 0.75 = Rs. 57, still not Rs. 60. 84 kg: Profit would be 84 * 0.75 = Rs. 63, which is greater than Rs. 60. Thus only 80 kg gives the correct profit of Rs. 60. Common Pitfalls: Students sometimes treat profit percent as a percentage of selling price instead of cost price, which is wrong here. Another frequent mistake is to try to work directly with percentages without first finding the cost price, which makes the calculations confusing. Forgetting that profit per kilogram is needed before using the total profit formula can also lead to errors. Final Answer: The total quantity of tea sold is 80 kg.

Question 15

The selling price of a cellphone is increased by 20 percent, and as a result the number of units sold decreases by 30 percent. What is the net percentage change in total sales revenue for the shopkeeper?

Accepted Answer

Introduction / Context: This problem tests understanding of percentage change in revenue when both price and quantity change. It is a classic type of question in profit and loss where candidates must recognize that revenue is the product of price and quantity, and changes in both factors can result in an overall gain or loss. Given Data / Assumptions: Original selling price of each cellphone = P (assumed). Original number of units sold = Q (assumed). Price is increased by 20 percent, so new price = 1.20 * P. Quantity sold decreases by 30 percent, so new quantity = 0.70 * Q. We need the net percentage change in total sales revenue. Concept / Approach: Total revenue is calculated as price multiplied by quantity. When both price and quantity change, the new revenue is the product of the new price and new quantity. The percentage change in revenue is then found by comparing new revenue with old revenue using the standard percentage change formula. Step-by-Step Solution: Original revenue = P * Q. New price after 20 percent increase = 1.20 * P. New quantity after 30 percent decrease = 0.70 * Q. New revenue = (1.20 * P) * (0.70 * Q) = 0.84 * P * Q. Thus new revenue is 84 percent of the original revenue. Percentage change in revenue = (new - old) / old * 100. Percentage change = (0.84 * P * Q - 1 * P * Q) / (P * Q) * 100. Percentage change = (0.84 - 1.00) * 100 = -16 percent. This means there is a 16 percent decrease in total sales revenue. Verification / Alternative check: Take convenient numbers: let P = Rs. 100 and Q = 10 units. Original revenue = 100 * 10 = Rs. 1000. New price = 120 rupees, new quantity = 7 units. New revenue = 120 * 7 = Rs. 840. Change in revenue = 840 - 1000 = -160 rupees. Percentage change = -160 / 1000 * 100 = -16 percent. This confirms a 16 percent loss in revenue. Why Other Options Are Wrong: 14.5%: This value does not match the product of the two percentage multipliers. 12% and 10.5%: These are smaller decreases and typically result from incorrect addition or subtraction of percentage values instead of multiplying them. Only 16 percent correctly reflects the combined effect of a 20 percent increase in price and a 30 percent fall in quantity. Common Pitfalls: Candidates sometimes add or subtract percentages directly, for example doing 20 percent minus 30 percent to get 10 percent, which is completely wrong in a revenue problem. Another common error is to forget that percentage changes in price and quantity must be combined multiplicatively, not additively. Always use the formula new revenue factor = price factor * quantity factor. Final Answer: The total sales revenue decreases by 16%, so the net effect is a 16 percent loss.

Question 16

Shamma lends a total of Rs. 40,000 to two friends. She lends Rs. 24,000 to the first friend at 8 percent per annum simple interest and wants an overall return of 10 percent per annum on the entire amount. At what simple interest rate should she lend…

Accepted Answer

Introduction / Context: This question checks the concept of weighted average interest rates in simple interest problems. The investor, Shamma, invests different portions of her total capital at different rates and aims for a specific overall return. Such questions are important in banking and finance related aptitude tests. Given Data / Assumptions: Total amount lent = Rs. 40,000. Amount lent to the first friend = Rs. 24,000 at 8 percent per annum simple interest. Remaining amount lent to the second friend = Rs. 40,000 - Rs. 24,000 = Rs. 16,000. Desired overall rate of return on the entire amount = 10 percent per annum. Time period for both loans is assumed to be the same, so it cancels out in calculations. Concept / Approach: Under simple interest, interest earned is directly proportional to principal, rate, and time. Since time is the same, the total interest can be treated as a weighted sum of interest from each part. The overall effective rate can be expressed as total interest divided by total principal. By equating desired total interest to the sum of interests from the two parts, we can solve for the unknown rate for the second friend. Step-by-Step Solution: Let R percent be the simple interest rate for the second friend. Total principal = 40,000 rupees. Desired overall interest for one year = 40,000 * 10 / 100 = 4,000 rupees. Interest from the first friend = 24,000 * 8 / 100 = 1,920 rupees. Interest needed from the second friend = total desired interest - first interest. Interest from second friend = 4,000 - 1,920 = 2,080 rupees. Principal given to the second friend = 16,000 rupees. So 16,000 * R / 100 = 2,080. R = (2,080 * 100) / 16,000 = 13 percent. Verification / Alternative check: Interest at 13 percent on Rs. 16,000 for one year = 16,000 * 13 / 100 = 2,080 rupees. Total interest from both loans = 1,920 + 2,080 = 4,000 rupees. Overall rate = 4,000 / 40,000 * 100 = 10 percent. This matches the desired overall rate, so the calculation is correct. Why Other Options Are Wrong: 8.5% and 9.5%: These rates are too low and will not generate enough interest from the second loan to reach a 10 percent overall return. 11.25%: This is closer but still insufficient; the total interest would be less than 4,000 rupees. Only 13 percent gives exactly the overall 10 percent simple interest on the total investment. Common Pitfalls: Many candidates mistakenly take a simple average of 8 percent and 10 percent or misapply the weighted average concept. Some also forget that the invested amounts are different, which makes the average rate weighted, not simple. Ignoring the total desired interest and directly averaging rates always leads to incorrect answers in these types of problems. Final Answer: The remaining sum must be lent at a simple interest rate of 13%.

Question 17

Raghu earns a profit of 25 percent on one investment but incurs a loss of 10 percent on another investment. The ratio of the amounts invested in the two cases is 3 : 5 respectively. What is the overall percentage gain or loss on both investments tak…

Accepted Answer

Introduction / Context: This question examines the idea of overall profit or loss when different parts of capital are invested at different profit or loss percentages. The key is to treat the problem as a weighted average percentage gain or loss, based on the proportions of total capital invested in each case. Given Data / Assumptions: Profit on the first investment = 25 percent. Loss on the second investment = 10 percent. Ratio of the first investment to the second investment = 3 : 5. We assume the same time period and no other costs or incomes. Concept / Approach: When there are two investments with different profit rates, the overall profit is the sum of the individual profits. Because the invested amounts are in a ratio, we can assume convenient values proportional to that ratio, such as 3x and 5x. Then, compute individual profit or loss in terms of x, add them, and finally divide by total investment to get the overall percentage gain or loss. Step-by-Step Solution: Assume first investment = 3x and second investment = 5x. Profit on the first investment = 25 percent of 3x = 0.25 * 3x = 0.75x. Loss on the second investment = 10 percent of 5x = 0.10 * 5x = 0.50x. Net profit = profit - loss = 0.75x - 0.50x = 0.25x. Total capital invested = 3x + 5x = 8x. Overall percentage gain = (net profit / total capital) * 100. Overall gain percent = (0.25x / 8x) * 100 = (0.25 / 8) * 100. 0.25 / 8 = 0.03125, so overall gain = 3.125 percent. Verification / Alternative check: Take x = 1000 for convenience. First investment = Rs. 3000, profit = 25 percent of 3000 = Rs. 750. Second investment = Rs. 5000, loss = 10 percent of 5000 = Rs. 500. Net profit = 750 - 500 = Rs. 250. Total investment = 3000 + 5000 = Rs. 8000. Overall gain percent = 250 / 8000 * 100 = 3.125 percent. This confirms the result. Why Other Options Are Wrong: 1.251 % and 7.21 % and 9.451 %: These values do not correspond to the correct weighted average calculation using the given ratio 3 : 5. They usually come from incorrect manipulation of percentages or from averaging the rates without considering the different investment amounts. Common Pitfalls: A common error is to average 25 percent and minus 10 percent directly to get 7.5 percent, which ignores the investment ratio. Another typical mistake is to treat the loss percentage as if it were on the same base amount as the profit percentage. Always use assumed values based on the given ratio to create a consistent base for both investments. Final Answer: The overall result is a net gain of 3.125 % on the combined investments.

Question 18

A man sells two flats for Rs. 4.15 lakhs each. On the first flat he gains 2 percent and on the second flat he loses 2 percent. What is the net percentage effect on his overall transaction for both flats together?

Accepted Answer

Introduction / Context: This question tests an important profit and loss concept where equal selling prices are involved but one item is sold at a gain and the other at a loss. In such cases the seller always incurs a net loss, and the percentage loss has a special formula which often appears in competitive exams. Given Data / Assumptions: Selling price of each flat = Rs. 4.15 lakhs. Gain on the first flat = 2 percent. Loss on the second flat = 2 percent. Total number of flats sold = 2. We need the net percentage gain or loss on the combined transaction. Concept / Approach: When two items are sold at the same selling price, and one yields a gain of x percent while the other yields a loss of x percent, the overall result is always a loss. The approximate net loss percent is given by x^2 / 100. This result can also be derived by computing the individual cost prices from the given selling prices and then comparing total cost and total selling price. Step-by-Step Solution: Let the common selling price of each flat be S. For the first flat, gain is 2 percent, so S = 1.02 * cost price of flat one. Thus cost price of flat one = S / 1.02. For the second flat, loss is 2 percent, so S = 0.98 * cost price of flat two. Thus cost price of flat two = S / 0.98. Total cost price = S / 1.02 + S / 0.98. Total selling price = S + S = 2S. Instead of heavy calculation, we use the known result: net loss percent = (2^2 / 100) = 4 / 100 = 0.04 percent. Verification / Alternative check: Take a convenient selling price S = Rs. 100. First flat: S = 100 is 2 percent above cost, so cost = 100 / 1.02 ≈ 98.04. Second flat: S = 100 is 2 percent below cost, so cost = 100 / 0.98 ≈ 102.04. Total cost ≈ 98.04 + 102.04 ≈ 200.08. Total selling price = 100 + 100 = 200. Loss ≈ 0.08 on a cost of 200, which is 0.04 percent loss. This confirms the formula based result. Why Other Options Are Wrong: 0.25 % and 0.5 %: These are larger magnitudes and result from incorrect approximations or from wrongly averaging gains and losses. 0 %: This assumes gains and losses cancel completely, which is not true when selling price is the same for both items. Only 0.04 percent correctly reflects the very small net loss. Common Pitfalls: A typical mistake is to assume that a 2 percent gain and a 2 percent loss cancel out, leading to zero net effect. This is incorrect because the base amounts for gain and loss (their cost prices) are different. Another common error is to average the percentages directly without using the correct relationship or formula. Remember the special case formula x^2 / 100 for equal selling prices with equal gain and loss percentages. Final Answer: The overall effect is a very small net loss of 0.04 %, not a gain.

Question 19

The cost price of 22 articles is equal to the selling price of 18 articles of the same type. What is the percentage profit made by the seller on each article?

Accepted Answer

Introduction / Context: This problem involves comparing total cost price and total selling price for different quantities of the same article. It is a standard type of profit percentage question, frequently used to test understanding of proportional reasoning and the relationship between cost price and selling price. Given Data / Assumptions: Cost price of 22 articles together = total CP. Selling price of 18 articles together = total SP. Given that total CP of 22 articles = total SP of 18 articles. All articles are identical and sold at the same rate, and there are no extra costs. Concept / Approach: If the cost of 22 articles equals the selling price of only 18 articles, it means that selling one article brings more revenue than its cost price. From this equality we can find the selling price of one article in terms of its cost price. Then the percentage profit is calculated as the difference between selling price and cost price divided by cost price, multiplied by 100. Step-by-Step Solution: Let cost price of one article be C. Then total cost price of 22 articles = 22 * C. Let selling price of one article be S. Then total selling price of 18 articles = 18 * S. Given: 22 * C = 18 * S. So S = (22 / 18) * C = (11 / 9) * C. Profit per article = S - C = (11 / 9) * C - C = (2 / 9) * C. Profit percentage = (profit / cost price) * 100. Profit percent = ((2 / 9) * C / C) * 100 = (2 / 9) * 100 ≈ 22.22 percent. Verification / Alternative check: Assume C = Rs. 9 for convenience. Then total cost of 22 articles = 22 * 9 = Rs. 198. This equals total selling price of 18 articles, so SP per article S = 198 / 18 = Rs. 11. Profit per article = 11 - 9 = Rs. 2. Profit percent = 2 / 9 * 100 ≈ 22.22 percent. This confirms the result. Why Other Options Are Wrong: 33.33%: This is larger than the true profit and comes from misinterpreting the ratio 22 : 18 as the direct profit percentage. 11.11% and 1%: These are too small and arise from arithmetic mistakes or incorrect use of ratios. Only 22.22 percent matches the correct calculation. Common Pitfalls: A common error is to think that profit percent is based on the difference between 22 and 18 directly. Candidates may also mistakenly treat 22 : 18 as the ratio of selling price to cost price instead of cost price to selling price, or forget that cost price is the base for profit percentage. Always identify which side of the equation represents cost and which represents selling price before computing percentages. Final Answer: The seller makes a profit of approximately 22.22% on each article.

Question 20

Mr. X sells two properties P1 and P2 for Rs. 1,00,000 each. He sells property P1 at a loss of 20 percent on its cost price. What percentage profit must he earn on property P2 so that overall there is neither gain nor loss on the sale of both propert…

Accepted Answer

Introduction / Context: This question illustrates how a loss on one item affects the required profit on another item when the seller wants to break even on the entire transaction. It tests understanding of cost price, selling price, and net gain or loss when two sales at the same selling price are involved. Given Data / Assumptions: Selling price of property P1 = Rs. 1,00,000. Selling price of property P2 = Rs. 1,00,000. Property P1 is sold at a loss of 20 percent. There is no overall gain or loss on both properties combined, so total selling price equals total cost price. Concept / Approach: If the selling prices are equal for both properties, then we can compute the cost price of P1 using the given loss percentage. Then we know the total cost price of both properties must equal the total selling price (because net result is no profit, no loss). This allows us to find the cost price of P2. Finally we compute the percentage profit on P2 required to offset the loss on P1. Step-by-Step Solution: Let C1 be the cost price of property P1. Loss on P1 = 20 percent, so selling price of P1 = C1 * (1 - 20 / 100) = 0.80 * C1. Given selling price of P1 = Rs. 1,00,000, so 1,00,000 = 0.80 * C1. Thus C1 = 1,00,000 / 0.80 = Rs. 1,25,000. Let C2 be the cost price of property P2. Total selling price of both properties = 1,00,000 + 1,00,000 = Rs. 2,00,000. Since there is no overall gain or loss, total cost price must also be Rs. 2,00,000. Therefore C1 + C2 = 2,00,000. So C2 = 2,00,000 - 1,25,000 = Rs. 75,000. Profit on property P2 = 1,00,000 - 75,000 = Rs. 25,000. Profit percentage on P2 = 25,000 / 75,000 * 100 = 33.33 percent. Verification / Alternative check: Total cost price = 1,25,000 + 75,000 = 2,00,000. Total selling price = 1,00,000 + 1,00,000 = 2,00,000. Net gain or loss = 2,00,000 - 2,00,000 = 0. This confirms that a profit of 33.33 percent on P2 exactly cancels the 20 percent loss on P1, producing no overall profit or loss. Why Other Options Are Wrong: 29.97% and 25% and 22.22%: These profit rates do not generate enough profit on P2 to counterbalance the 20 percent loss on P1, so the overall transaction would still result in a net loss. Only 33.33 percent gives perfect balance. Common Pitfalls: One common mistake is to try to average the percentage loss and percentage profit directly. Another error is to assume equal cost prices instead of equal selling prices. Remember that equal selling prices with unequal gain or loss percentages always require careful calculation of cost prices for each item. Final Answer: He must make a profit of 33.33% on property P2 to have no overall gain or loss.

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