Question 1

The selling price of a fan is Rs 4644 and on this sale the seller earns a profit of 29% on the cost price. What is the cost price of the fan (in rupees)?

Accepted Answer

Introduction / Context:This question tests the ability to compute cost price when selling price and profit percentage are given. It is a direct reverse percentage problem that appears regularly in basic profit and loss sections of aptitude exams. Understanding how to express selling price in terms of cost price and profit percentage is the key to solving such questions quickly. Given Data / Assumptions: Selling price SP = Rs 4644. Profit percentage on cost price = 29%. Cost price CP is unknown and needs to be determined. Profit is calculated as SP - CP. Concept / Approach:If profit percentage is p, then selling price is equal to (100 + p)% of the cost price. In this question, SP = 129% of CP. Therefore CP can be obtained by dividing SP by 1.29. Once CP is calculated, we can check that adding 29% of CP does indeed yield the given selling price. This simple ratio relationship is a standard approach for these kinds of problems. Step-by-Step Solution:Step 1: Let CP be the cost price.Step 2: Profit percentage is 29%, so SP = 129% of CP = 1.29 * CP.Step 3: Given SP = 4644.Step 4: Therefore 1.29 * CP = 4644.Step 5: CP = 4644 / 1.29.Step 6: Compute CP: 4644 / 1.29 = 3600.Step 7: Hence the cost price of the fan is Rs 3600. Verification / Alternative check:We can verify by recomputing the selling price from the cost price. If CP = 3600, then profit at 29% is 0.29 * 3600 = 1044. New SP should be CP + profit = 3600 + 1044 = 4644, which exactly matches the given selling price. This confirms that our calculated cost price is correct and that we have used the percentage relation properly. Why Other Options Are Wrong:Option A (5900), option B (3500) and option C (3800) do not satisfy the condition that 29% of CP added to CP equals 4644. For example, 29% of 3500 is 1015, giving an SP of 4515, not 4644. Similarly, 29% of 3800 is 1102, giving 4902, which also does not match. Only option D, 3600, fits exactly with the given selling price and profit percentage. Common Pitfalls:Some learners mistakenly treat 29% of the selling price as the profit instead of 29% of the cost price, which gives incorrect results. Others subtract 29 from 4644 or perform other unrelated operations. Always remember that profit or loss percentage is based on cost price unless explicitly stated otherwise. Writing SP = (100 + p)% of CP is a good habit to avoid confusion. Final Answer:The cost price of the fan is Rs 3600.

Question 2

A man buys 25 crates of oranges for a total of Rs 10,000. Unfortunately, 5 crates are completely spoiled and cannot be sold. To earn an overall profit of 25% on his total cost, at what price should he sell each of the remaining crates?

Accepted Answer

Introduction / Context:This question combines the idea of total investment with losses due to spoilage and desired overall profit on the entire investment. The man buys a set of crates, loses some due to spoilage, and must adjust the selling price of the remaining crates to achieve a target profit percentage on the original cost. This is a standard type of problem in profit and loss related to damaged goods and effective pricing. Given Data / Assumptions: Total crates bought = 25. Total cost = Rs 10,000. Number of crates spoiled and unsellable = 5. Number of crates remaining for sale = 25 - 5 = 20. Desired overall profit on total cost = 25%. We must find the selling price per remaining crate. Concept / Approach:First determine the total revenue required to achieve a 25% profit on the initial investment of Rs 10,000. That revenue must be obtained by selling the remaining 20 crates, since 5 crates are completely spoiled. Then divide the required total revenue by the number of sellable crates to get the selling price per crate. The key idea is that the entire cost, including the cost of spoiled crates, has to be recovered along with the target profit from the crates that are actually sold. Step-by-Step Solution:Step 1: Total cost price TCP = Rs 10,000.Step 2: Desired profit percentage = 25%.Step 3: Desired profit amount = 25% of 10,000 = 0.25 * 10,000 = Rs 2,500.Step 4: Required total revenue (total selling price) = TCP + profit = 10,000 + 2,500 = Rs 12,500.Step 5: Number of good crates available for sale = 20.Step 6: Selling price per crate needed = Total revenue / number of sellable crates = 12,500 / 20.Step 7: 12,500 / 20 = 625.Step 8: Therefore each of the remaining crates must be sold at Rs 625. Verification / Alternative check:We can check the overall profit if each of the 20 crates is sold at Rs 625. Total selling revenue = 20 * 625 = Rs 12,500. Subtracting the original cost of Rs 10,000, we get a profit of Rs 2,500. The profit percentage is 2,500 / 10,000 * 100 = 25%, which matches the desired overall profit. This verifies that the computed price per crate is correct. Why Other Options Are Wrong:Option A (Rs 650) would give total revenue of 20 * 650 = Rs 13,000, which corresponds to a profit of Rs 3,000 or 30%, higher than the required 25%. Option C (Rs 600) yields 20 * 600 = Rs 12,000, which is a 20% profit only. Option D (Rs 575) gives 11,500 total revenue, just 15% profit. Only option B, Rs 625 per crate, produces exactly a 25% profit on the total cost. Common Pitfalls:Students sometimes calculate profit only on the remaining crates and ignore the cost of spoiled crates, which underestimates the required selling price. Others divide the original cost by the remaining crates instead of calculating the revenue required for the desired profit. It is important to remember that spoilage still counts as part of the investment, and the target profit is based on the total initial cost, not only on the cost of the unsplit portion. Final Answer:He should sell each of the remaining crates at Rs 625 to earn a 25% overall profit.

Question 3

A dishonest shopkeeper claims to sell goods at cost price but uses a false weight of 950 grams instead of a true kilogram (1000 grams). What is his gain percentage in this situation?

Accepted Answer

Introduction / Context:This is a typical question on cheating in weights and measures. The shopkeeper pretends to sell one kilogram but actually gives only 950 grams while charging the full price of 1 kilogram. Such questions test understanding of effective selling price and cost price per true unit and how this creates a hidden profit percentage even when the claimed selling price matches the stated cost price. Given Data / Assumptions: Shopkeeper claims to sell 1 kilogram of goods at cost price. Actual quantity given to the customer is 950 grams. Customer pays the price meant for 1000 grams. Let the cost price of 1 kilogram be C rupees. We need the gain percentage based on true cost. Concept / Approach:If 1 kilogram costs C rupees, then the cost of 950 grams is proportional. The dishonest shopkeeper collects C rupees from the customer but spends only the cost of 950 grams. The difference between these two amounts is the hidden profit. Profit percentage is computed as (Profit / Cost of goods actually given) * 100. The key is to treat 950 grams as the real cost basis, since that is the amount of goods actually delivered. Step-by-Step Solution:Step 1: Let cost price of 1000 grams (1 kilogram) be C rupees.Step 2: Cost price of 1 gram = C / 1000.Step 3: Cost price of 950 grams = 950 * (C / 1000) = 0.95C.Step 4: The shopkeeper sells 950 grams but charges for 1000 grams at cost price, so selling price SP = C rupees.Step 5: Profit = SP - CP of goods actually sold = C - 0.95C = 0.05C.Step 6: Profit percentage = (Profit / CP) * 100 = (0.05C / 0.95C) * 100.Step 7: Simplify ratio: 0.05 / 0.95 = 5 / 95 = 1 / 19.Step 8: Profit percentage = (1 / 19) * 100 = 100 / 19%. Verification / Alternative check:We can use a numerical example. Assume C = Rs 100 for 1 kilogram. Then the cost of 950 grams is 0.95 * 100 = Rs 95. The shopkeeper collects Rs 100 from the customer. Profit = 100 - 95 = Rs 5. Profit percentage = 5 / 95 * 100 ≈ 5.263%, which is exactly 100 / 19%. This numerical confirmation verifies the algebraic steps and shows that the answer is precise. Why Other Options Are Wrong:Option A (100/23%), option C (100/17%) and option D (100/21%) are all close looking fractions but none match the ratio 5 / 95. Only 100 / 19 corresponds to the exact fraction (1/19) * 100 obtained from the correct computation. The other denominators represent different hidden profit margins that would arise from different false weights, not the given 950 grams case. Common Pitfalls:A common mistake is to compute profit percentage with base 1000 grams instead of the 950 grams actually supplied, which leads to a smaller and incorrect percentage. Others incorrectly assume that the profit is exactly 5% without accounting for the smaller base. Always remember that percentage profit is calculated on the cost of goods actually given away, which in cheating questions is usually lower than the claimed quantity. Final Answer:The dishonest shopkeeper gains 100/19% profit by using the 950 gram weight instead of a true kilogram.

Question 4

A dishonest dealer claims to sell goods at cost price but actually uses a weight of only 875 grams instead of a true kilogram (1000 grams). What is his gain in percentage?

Accepted Answer

Introduction / Context:This cheating problem is similar to the previous one but with a different false weight. The dealer pretends to sell 1 kilogram but actually delivers only 875 grams, while charging the price of 1 kilogram at the supposed cost price. It tests the ability to compute effective profit percentage when the quantity delivered is less than the quantity charged and to express the final answer as a mixed fraction percent. Given Data / Assumptions: Dealer claims to sell 1 kilogram at cost price. Actual quantity delivered is 875 grams. Customer pays for 1000 grams at cost price. Let the cost price of 1 kilogram be C rupees. We need the gain percentage. Concept / Approach:As before, the dealer really spends only the cost of 875 grams, but charges the customer for 1000 grams. So selling price is C rupees, and cost price of the goods actually delivered is proportional to 875 grams. The profit is the difference between these two amounts. Profit percentage is calculated on the cost of 875 grams, not on the cost of 1 kilogram. The fraction obtained must then be converted into a percentage and simplified into a mixed fraction form like 14 2/7%. Step-by-Step Solution:Step 1: Let cost price of 1000 grams be C rupees.Step 2: Cost per gram = C / 1000.Step 3: Cost of 875 grams = 875 * (C / 1000) = 0.875C.Step 4: Selling price SP for claimed 1 kilogram = C rupees.Step 5: Profit = SP - CP = C - 0.875C = 0.125C.Step 6: Profit percentage = (0.125C / 0.875C) * 100.Step 7: Ratio 0.125 / 0.875 = 125 / 875 = 1 / 7.Step 8: Therefore profit percentage = (1 / 7) * 100 = 100 / 7%.Step 9: 100 / 7 = 14 2/7% when expressed as a mixed fraction. Verification / Alternative check:Use a numerical example with C = Rs 100 for 1000 grams. Cost of 875 grams = 87.5 rupees. The dealer charges Rs 100. Profit = 100 - 87.5 = 12.5 rupees. Profit percentage = 12.5 / 87.5 * 100 = (1 / 7) * 100 = 14 2/7%. This matches the algebraic result quite precisely and confirms the correctness of our computations and the fraction simplification. Why Other Options Are Wrong:Option A (17%) is larger than the correct value and would correspond to a much smaller true quantity being given. Option B (14 5/7%) is close but still slightly larger than the true percentage and corresponds to a different false weight. Option D (14%) is a rounded value and does not exactly match the fraction 1/7. Only option C, 14 2/7%, correctly represents 100 / 7% and matches our detailed calculations. Common Pitfalls:Some candidates take profit percentage over 1000 grams instead of 875 grams, leading to 12.5% instead of 14 2/7%. Others incorrectly reduce the fraction or round too early, which causes them to miss the precise mixed fraction form. Always compute profit percentage on the cost of actual goods given and only simplify fractions at the end to avoid rounding errors. Final Answer:The dishonest dealer gains 14 2/7% by using an 875 gram weight instead of a true kilogram.

Question 5

A shopkeeper marks his goods 50% above the cost price and then allows a discount of 25% on the marked price. What is his net profit or loss percentage on the cost price?

Accepted Answer

Introduction / Context:This question examines the combined effect of a markup and a discount on the overall profit or loss percentage. The shopkeeper first increases the price by a certain percentage to set the marked price and then gives a discount on that marked price. The net effect on profit is calculated with respect to the cost price. This is a typical exam question and helps strengthen the understanding of successive percentage changes applied on different bases. Given Data / Assumptions: Goods are marked 50% above cost price. A discount of 25% is allowed on the marked price. We must find the overall profit or loss percentage on the cost price. Assume cost price CP = 100 units for simplicity. Concept / Approach:First compute the marked price by applying a 50% increase on cost price. Then apply a 25% discount on that marked price to get the selling price. Since profit and loss are based on cost price, we compare the final selling price with the original cost price to find the percentage profit or loss. This procedure is a straightforward application of percentage multipliers: one for markup, another for discount. Step-by-Step Solution:Step 1: Let CP = 100.Step 2: Marked price MP = CP + 50% of CP = 100 + 50 = 150.Step 3: Discount = 25% of MP.Step 4: Selling price SP = MP - 25% of MP = 150 - 0.25 * 150.Step 5: 0.25 * 150 = 37.5, so SP = 150 - 37.5 = 112.5.Step 6: Profit = SP - CP = 112.5 - 100 = 12.5.Step 7: Profit percentage = (12.5 / 100) * 100 = 12.5%.Step 8: Therefore there is a net profit of 12.5%. Verification / Alternative check:Another way is to use multipliers: a 50% markup corresponds to multiplying cost price by 1.5. A 25% discount corresponds to multiplying marked price by 0.75. Effective multiplier from cost to selling price is 1.5 * 0.75 = 1.125. This means SP = 112.5 when CP = 100, confirming a 12.5% profit. Both calculation styles lead to the same result, verifying the correctness of the answer. Why Other Options Are Wrong:Option A (37.5%) confuses the discount amount with the profit. Option B (25.5%) is a random value not supported by the calculation. Option D (25%) would be correct if markup and discount completely cancelled each other in a certain way, which they do not here. Only option C, 12.5%, matches the effective multiplier and the step-by-step numerical calculation. Common Pitfalls:Some learners mistakenly add or subtract the percentage values directly (for example, 50% minus 25% equals 25% profit), which ignores the different bases of these percentages. Others apply both percentages on cost price instead of on cost and marked price separately. Always be clear about what each percentage is applied to and use multipliers to avoid confusion with successive percentage changes. Final Answer:The shopkeeper makes a net 12.5% profit on the cost price.

Question 6

If a 10% loss is made on the selling price of an article, what will be the corresponding rate of loss on the cost price?

Accepted Answer

Introduction / Context:This question tests the ability to switch between loss defined as a percentage of selling price and loss defined as a percentage of cost price. Usually in profit and loss questions, percentages are given with respect to cost price, but here the loss is specified as a fraction of the selling price. Converting between these two bases is a useful skill for percentage arithmetic in aptitude exams. Given Data / Assumptions: Loss is 10% of the selling price (SP). We have to find loss percentage with respect to cost price (CP). Let selling price be S units. Loss amount = 10% of S = 0.10S. Concept / Approach:Loss is the difference between cost price and selling price. If loss is given as a fraction of selling price, we can express cost price as selling price plus this loss. Then loss percentage on cost price is calculated as (Loss / Cost price) * 100. The key is to express both cost price and loss in terms of the same variable, here S, and then form the required ratio. Step-by-Step Solution:Step 1: Let selling price S be some positive value (for example S units).Step 2: Given that loss is 10% of S, so Loss = 0.10S.Step 3: Since loss = CP - SP, we have CP = SP + Loss = S + 0.10S = 1.10S.Step 4: Now express loss percentage on cost price: Loss% = (Loss / CP) * 100.Step 5: Substitute: Loss% = (0.10S / 1.10S) * 100.Step 6: Simplify the ratio: 0.10S / 1.10S = 10 / 110 = 1 / 11.Step 7: Therefore Loss% = (1 / 11) * 100 = 100 / 11%.Step 8: 100 / 11 = 9 1/11% approximately 9.09%. Verification / Alternative check:Take a simple numerical value for S, such as S = 100. Then loss = 10% of 100 = 10. Thus CP = S + Loss = 100 + 10 = 110. Loss percentage with respect to cost price is Loss / CP * 100 = 10 / 110 * 100 = 100 / 11% = 9 1/11%. This exactly matches the algebraic derivation, confirming that the conversion is correct and that the loss percentage on cost price is slightly below 10%. Why Other Options Are Wrong:Option A (11 1/9%) and option D (11%) are both greater than 10%, which cannot happen when loss is defined as 10% of selling price because cost price is larger than selling price, making the percentage on cost lower. Option C (10%) simply repeats the given loss percentage on selling price and ignores the change of base to cost price. Only option B correctly translates the 10% loss on selling price into a 9 1/11% loss on cost price. Common Pitfalls:Many students mistakenly assume that the loss percentage remains the same when switching from selling price to cost price as base. Others invert the relationship and end up with a higher percentage like 11% or more. Always remember that when CP is greater than SP, a given loss expressed as a percentage of the smaller value (SP) will convert into a smaller percentage when expressed relative to the larger value (CP). Working through the algebra carefully prevents such base confusion. Final Answer:The rate of loss on the cost price is 9 1/11%.

Question 7

A dealer purchases an article for Rs 900 and fixes the list price so that he can still gain 20% on cost price even after allowing a 10% discount on the list price. What should be the list price of the article?

Accepted Answer

Introduction / Context:This question involves determining the list price needed to achieve a desired net profit after giving a discount. The dealer wants a 20% gain on cost price even after allowing a 10% discount on the marked price. Such problems are very common in profit and loss chapters to test multi step reasoning with cost price, marked price, discount and profit percentage. Given Data / Assumptions: Cost price CP = Rs 900. Desired profit percentage = 20% on cost. Dealer allows a discount of 10% on the list price (marked price). We must find the list price (marked price) that satisfies these conditions. Concept / Approach:First compute the selling price required to achieve a 20% profit on cost. Then use the given discount percentage to find what the list price must be so that, after discounting, the selling price equals this target value. The relationship between selling price and list price is given by SP = (1 - discount rate) * List price. Rearranging this equation gives the necessary list price once the desired selling price is known. Step-by-Step Solution:Step 1: Cost price CP = 900.Step 2: Desired profit = 20% of CP = 0.20 * 900 = 180.Step 3: Required selling price SP = CP + profit = 900 + 180 = Rs 1080.Step 4: The dealer gives a discount of 10% on the list price.Step 5: Let list price be LP. Then SP = LP - 10% of LP = 0.90 * LP.Step 6: Substitute SP = 1080 into 0.90 * LP = 1080.Step 7: LP = 1080 / 0.90 = 1200.Step 8: Therefore the list price must be Rs 1200. Verification / Alternative check:We can verify quickly. If LP = 1200, a 10% discount is 120. So SP = 1200 - 120 = 1080. Comparing SP with CP of 900, profit = 1080 - 900 = 180. Profit percentage is 180 / 900 * 100 = 20%, exactly as required. This confirms that the chosen list price produces the correct net profit after discount. Why Other Options Are Wrong:Option A (Rs 1180), option B (Rs 1080) and option D (Rs 1100) all give selling prices which either do not match 1080 after a 10% discount or do not yield a 20% profit when compared to CP of 900. Only LP = 1200 gives SP = 1080 and leads to a 20% profit, so option C is the only correct choice. Common Pitfalls:Students sometimes mistakenly take 20% profit directly on the list price or subtract both 20% and 10% from the cost price without understanding that profit is computed on CP and discount is computed on list price. Others treat selling price as list price minus 20% instead of 10%. Clearly writing each relation and stating the base of each percentage helps avoid these typical errors. Final Answer:The dealer should fix the list price at Rs 1200.

Question 8

The cost price of 28 articles is equal to the selling price of 21 articles of the same kind. What is the percentage of profit made by the seller?

Accepted Answer

Introduction / Context:This question is about comparing total cost and total selling price for different quantities of the same article. The condition that the cost of a larger number of articles equals the sales revenue of a smaller number indicates a profit on each article. The goal is to compute the profit percentage per article, which is a standard type in profit and loss topics using ratio and proportion concepts. Given Data / Assumptions: Cost price of 28 articles equals selling price of 21 articles. All articles are identical in cost and selling price behavior. Let cost price per article be C and selling price per article be S. We need to find profit percentage on cost price. Concept / Approach:Since the articles are identical, we can express total cost and total selling price in terms of per article prices and number of articles. Then use the equality between total cost of 28 and total selling price of 21 to find the ratio of S to C. Once this ratio is known, profit per article is S - C and the profit percentage is (S - C) / C * 100. This approach avoids needing any actual currency values and relies purely on ratios. Step-by-Step Solution:Step 1: Let cost price per article = C.Step 2: Let selling price per article = S.Step 3: Total cost of 28 articles = 28C.Step 4: Total selling price of 21 articles = 21S.Step 5: Given that 28C = 21S.Step 6: Divide both sides by 7: 4C = 3S.Step 7: Therefore S = (4/3) * C.Step 8: Profit per article = S - C = (4/3)C - C = (1/3)C.Step 9: Profit percentage = [(1/3)C / C] * 100 = (1/3) * 100 = 33 1/3 %. Verification / Alternative check:We can use notional values to confirm. Suppose C = Rs 3. Then S = (4/3) * 3 = Rs 4. Cost of 28 articles = 28 * 3 = Rs 84. Selling price of 21 articles = 21 * 4 = Rs 84, which satisfies the given condition. Profit per article is Rs 1 on a cost of Rs 3. Profit percentage is 1 / 3 * 100 = 33 1/3 %, confirming the earlier ratio based calculation. Why Other Options Are Wrong:Option A (12%), option C (20%) and option D (22%) are all smaller than the correct profit percentage and do not match the ratio S = 4C/3 implied by the equality 28C = 21S. Only option B, 33 1⁄3 %, exactly arises from the fraction (1/3)C and matches the derived profit percentage. Common Pitfalls:Students sometimes misinterpret the statement and reverse the relationship, such as equating cost of 21 items with selling price of 28 items, leading to a loss instead of a profit. Others may divide 28 by 21 or vice versa without linking correctly to per unit prices. Writing down the symbolic expressions for total cost and total selling price and then solving for S in terms of C is the safest way to handle such comparisons. Final Answer:The profit percentage made by the seller is 33 1⁄3 %.

Question 9

A vendor sells a coconut at Rs 24 and incurs a loss of 20%. If instead he sells a coconut at Rs 36, what will be his profit percentage?

Accepted Answer

Introduction / Context:This is a two stage profit and loss question. The vendor first sells a coconut at a loss, which allows us to reconstruct the cost price. Later, he sells at a higher price, and we must calculate the profit percentage. This type of question checks your ability to move from one selling situation to another by correctly identifying and reusing the cost price as a fixed reference point. Given Data / Assumptions: When the coconut is sold at Rs 24, there is a loss of 20%. When it is sold at Rs 36, we must find the profit percentage. Let CP be the cost price of one coconut. Loss and profit percentages are calculated on CP. Concept / Approach:Loss of 20% means the selling price is 80% of the cost price. Using this relation, we compute cost price from the first scenario. With the cost price known, we then compute the profit when the coconut is sold at the second selling price by the formula profit% = (SP - CP) / CP * 100. Identifying that CP is the same for both transactions is essential for the correct solution. Step-by-Step Solution:Step 1: Let cost price be CP.Step 2: At SP = 24, loss = 20%, so SP = 80% of CP = 0.80 * CP.Step 3: Thus 0.80 * CP = 24.Step 4: CP = 24 / 0.80 = 30.Step 5: Now consider SP2 = 36.Step 6: Profit when selling at 36 = SP2 - CP = 36 - 30 = 6.Step 7: Profit percentage = (6 / 30) * 100 = 20%.Step 8: Therefore the vendor earns a 20% profit when selling at Rs 36. Verification / Alternative check:We can verify reasoning by checking both cases around CP = 30. At SP = 24, the loss is 6 on 30, that is 6 / 30 * 100 = 20% loss, which matches the given. At SP = 36, the profit is also 6 on 30, that is 20% profit. This symmetry around the cost price confirms that the cost price is exactly midway between the two selling prices and that the profit percentage at Rs 36 is indeed 20%. Why Other Options Are Wrong:Option A (10), option C (30), and option D (40) do not match the computed profit percentage. A 10% profit would imply a cost price different from Rs 30, and 30% or 40% would require larger differences between SP and CP. Only option B, 20, correctly reflects the profit percentage when the cost price is Rs 30 and the selling price is Rs 36. Common Pitfalls:Some students incorrectly think that if 24 yields a 20% loss, then 36 might yield a 20% gain without checking the arithmetic. Others confuse which value is cost price and which is selling price when setting up the first equation. It is important to first solve precisely for cost price using the loss condition before jumping to conclusions about profit in the second case. Final Answer:When he sells a coconut at Rs 36, the vendor makes a 20% profit.

Question 10

A wholesaler sells a tin of coffee at Rs 528 and faces a loss of 12%. Later he decides to sell the same tin at Rs 636. What will be his profit percentage at this new selling price?

Accepted Answer

Introduction / Context:This problem involves two different selling prices for the same product, one at a loss and one at a profit. The wholesaler initially sells at a loss, which allows us to find the cost price. Then, with a higher selling price, we can determine the resulting profit percentage. Questions like this reinforce the method of first finding cost price from one known transaction and then reusing it for another transaction. Given Data / Assumptions: First selling price SP1 = Rs 528 with a 12% loss. Second selling price SP2 = Rs 636. Let CP be the cost price of the tin. We must calculate the profit percentage at SP2. Concept / Approach:A loss of 12% means that the selling price is 88% of the cost price. We can use SP1 = 0.88 * CP to find CP. After finding CP, the profit at SP2 is simply SP2 - CP, and the profit percentage is (SP2 - CP) / CP * 100. This two step approach is a standard technique for dealing with changed selling prices in profit and loss questions. Step-by-Step Solution:Step 1: Let CP be the cost price.Step 2: At SP1 = 528, loss = 12%, so SP1 = 88% of CP = 0.88 * CP.Step 3: Therefore 0.88 * CP = 528.Step 4: CP = 528 / 0.88 = 600.Step 5: Now consider SP2 = 636.Step 6: Profit at SP2 = 636 - 600 = 36.Step 7: Profit percentage = (36 / 600) * 100 = 6%.Step 8: Therefore the wholesaler makes a 6% profit at the selling price of Rs 636. Verification / Alternative check:To check, we verify the initial loss condition. If CP is 600, 12% of 600 is 72, so SP should be 600 - 72 = 528, which matches SP1. For SP2, if CP is 600 and SP is 636, profit is 36. The fraction 36 / 600 reduces to 6 / 100, giving 6%. This confirms that both the loss and profit calculations are correct and consistent with the given data. Why Other Options Are Wrong:Option A (7), option B (5) and option D (4) all represent profit percentages that do not match the exact ratio 36 / 600. A 7% profit would require a profit of 42 on a cost of 600, while a 5% profit would need a profit of 30. None of these would lead to a selling price of 636. Only option C, 6, is fully consistent with the numbers given in the question. Common Pitfalls:Some students incorrectly take 12% of 528 instead of 12% of cost price when reconstructing CP, which gives a wrong cost price. Others may miscalculate 528 / 0.88. It is important to remember that loss percentage is always on cost price unless explicitly stated otherwise, and that dividing the selling price by (1 - loss rate) is the correct way to find cost price from a loss scenario. Final Answer:At the new selling price of Rs 636, the wholesaler makes a 6% profit.

Question 11

A trader has 1200 kilograms of rice. He sells part of it at a profit of 5% and the rest at a profit of 11%, so that his overall profit on the entire quantity is 7%. How many kilograms of rice did he sell at 5% profit?

Accepted Answer

Introduction / Context:This question combines the idea of weighted average profit with quantities sold at different profit rates. The trader sells one part of the rice stock at a lower profit percentage and the remaining part at a higher profit percentage. The overall profit percentage on the entire stock is known. The aim is to find how much was sold at the lower profit rate. This type of question is common in mixture and alligation topics as well as profit and loss. Given Data / Assumptions: Total quantity of rice = 1200 kilograms. Some quantity is sold at 5% profit. The rest is sold at 11% profit. Overall profit on total 1200 kilograms = 7%. We need to find the quantity sold at 5% profit. Concept / Approach:The overall profit percentage is a weighted average of the individual profit percentages, with weights equal to the respective quantities sold. If x kilograms are sold at 5% profit and the remaining (1200 - x) kilograms at 11% profit, then the total profit percentage is given by [5x + 11(1200 - x)] / 1200. This must equal 7. Setting up this equation and solving for x yields the quantity sold at 5% profit. This is essentially a linear equation in one variable derived from the weighted average formula. Step-by-Step Solution:Step 1: Let x be the quantity sold at 5% profit.Step 2: Then quantity sold at 11% profit is 1200 - x kilograms.Step 3: Total profit (in percentage points times kilograms) = 5x + 11(1200 - x).Step 4: Overall profit percentage is 7, so this total profit divided by 1200 equals 7.Step 5: Write equation: (5x + 11(1200 - x)) / 1200 = 7.Step 6: Multiply both sides by 1200: 5x + 11(1200 - x) = 7 * 1200.Step 7: Expand: 5x + 13200 - 11x = 8400.Step 8: Combine like terms: (5x - 11x) + 13200 = 8400 gives -6x + 13200 = 8400.Step 9: Rearrange: -6x = 8400 - 13200 = -4800.Step 10: So x = (-4800) / (-6) = 800.Step 11: Therefore 800 kilograms of rice were sold at 5% profit. Verification / Alternative check:We can quickly verify using the found values. Rice at 5% profit: 800 kilograms. Rice at 11% profit: 1200 - 800 = 400 kilograms. Total profit in percentage points times kilograms = 5 * 800 + 11 * 400 = 4000 + 4400 = 8400. Overall profit percentage = 8400 / 1200 = 7%. This exactly matches the given overall profit percentage, confirming that the derived quantity of 800 kilograms is correct. Why Other Options Are Wrong:Option A (900) would give too much weight to the lower profit, reducing overall profit below 7%. Option B (600) would overweight the higher profit, pushing the overall percentage above 7%. Option C (400) would mean very little rice is sold at 5% profit and most at 11%, which again does not match the given 7% overall profit. Only option D, 800 kilograms, satisfies the weighted average condition required by the data. Common Pitfalls:Some students mistakenly average 5% and 11% directly to get 8% and then try to adjust, ignoring that different quantities are sold at each rate. Others mix up which quantity corresponds to which profit percentage. Writing the equation clearly with x and 1200 - x, and then carefully expanding and simplifying, is the safest way to avoid such errors. Using the alligation rule is also possible but requires careful handling of ratios and total quantity. Final Answer:The trader sells 800 kilograms of rice at a 5% profit.

Question 12

A saree is sold for Rs 1900 at a loss of 5%. At what selling price (in Rs) should the same saree be sold so that the seller makes a 15% profit on its cost price?

Accepted Answer

Introduction / Context: In profit and loss aptitude questions, it is very common to move between cost price, selling price, and profit or loss percentage. This question tests your understanding of how to reverse calculate the cost price from a known loss situation and then use that cost price to find a new selling price for a desired profit. Such questions are frequently asked in banking, SSC, and other competitive exams because they require clear understanding of percentage calculations and relationships between cost and selling prices. Given Data / Assumptions: The saree is sold for Rs 1900. At Rs 1900, the seller incurs a loss of 5%. We assume the cost price is the same in both transactions. We want a profit of 15% on the same cost price. We need to find the new selling price that gives 15% profit. Concept / Approach: The key ideas are: Loss percent = (Loss / Cost Price) * 100. If there is a loss of 5%, then Selling Price = 95% of Cost Price. If there is a profit of 15%, then Selling Price = 115% of Cost Price. Work in terms of the cost price first, then compute the required selling price. Step-by-Step Solution: Let the cost price of the saree be C. Given that selling at Rs 1900 causes a 5% loss, so 1900 = 0.95 * C. Therefore, C = 1900 / 0.95. Compute C: C = 2000. For a profit of 15%, the new selling price S should be S = 1.15 * C. S = 1.15 * 2000 = 2300. So, the saree must be sold for Rs 2300 to earn 15% profit. Verification / Alternative check: We can verify using direct profit calculation. With cost price 2000 and selling price 2300, profit = 2300 - 2000 = 300. Profit percent = (300 / 2000) * 100 = 15%. This matches the required profit percentage. For the first case, selling price 1900 gives loss = 2000 - 1900 = 100. Loss percent = (100 / 2000) * 100 = 5%, which matches the given information. Hence, the calculated cost price and new selling price are consistent and correct. Why Other Options Are Wrong: 2200 would give profit = 200, that is (200 / 2000) * 100 = 10%, not 15%. 2400 would give profit of 400, that is 20%. 2500 would give profit of 500, that is 25%. 2100 would give profit of 100, only 5%. Therefore, none of these options match the required 15% profit target. Common Pitfalls: A common mistake is to apply the percentage directly to 1900 instead of first finding the cost price. Another frequent error is to mix up loss percent and profit percent or to treat them as additive on the same selling price without working through the cost price. Careless handling of decimal multipliers like 0.95 and 1.15 can also create calculation errors. Always clearly define the cost price and work step by step from the given selling price and percentage information. Final Answer: Therefore, the saree should be sold for 2300 rupees to earn a 15% profit on its cost price.

Question 13

A shopkeeper sells 21 identical items and finds that his total profit is exactly equal to the selling price of 1 item. What is his percentage profit on each item?

Accepted Answer

Introduction / Context: This problem deals with the basic relationship between cost price, selling price, and profit percentage when multiple identical items are sold. Instead of giving direct numerical prices, the question uses a clever condition based on total profit and the selling price of one item. Such questions appear often in aptitude exams to test algebraic thinking and the ability to form equations from verbal statements. Given Data / Assumptions: All 21 items are identical. Total profit earned by selling 21 items equals the selling price of 1 item. We assume each item has the same cost price and selling price. We need to find the profit percentage on each item. Concept / Approach: We use the following ideas: Let cost price of one item be C and selling price be S. Total profit for 21 items is 21(S - C). Given that total profit = S. This condition leads to an equation that relates S and C. Once S in terms of C is known, profit percent = ((S - C) / C) * 100. Step-by-Step Solution: Let cost price of one item be C and selling price be S. Total profit for 21 items = 21(S - C). Given: 21(S - C) = S. Rearrange: 21S - 21C = S, so 20S = 21C. Thus S / C = 21 / 20. Profit on one item = S - C = (21/20)C - C = (1/20)C. Profit percent = ((S - C) / C) * 100 = (1/20) * 100 = 5%. Verification / Alternative check: Assume an easy cost price to verify, for example C = 20. Then S = (21/20) * 20 = 21. Profit per item is 1. For 21 items, total profit is 21 * 1 = 21. This is exactly equal to the selling price of 1 item, which is also 21. The condition in the question is satisfied, and the calculated profit percent is (1 / 20) * 100 = 5%. This confirms that our algebraic solution is correct. Why Other Options Are Wrong: If profit were 2% or 2.5%, S / C would be close to 1.02 or 1.025, which would not satisfy 21(S - C) = S. Similarly, 4% or 6% would yield different ratios that do not lead to total profit equalling the selling price of 1 item. Only a 5% profit ensures that total profit becomes exactly the price of one item. Common Pitfalls: Students often try random trial and error with percentages instead of forming the equation. Another mistake is misinterpreting the statement and equating profit per item to the selling price of one item instead of total profit to one selling price. Always translate the language of the problem into algebra calmly and then solve step by step. Final Answer: The shopkeeper makes a profit of 5% on each item.

Question 14

A trader has 630 kg of rice. He sells part of it at a profit of 15% and the remaining part at a profit of 8%, so that his overall profit on the entire quantity is 12%. How many kilograms of rice does he sell at 8% profit?

Accepted Answer

Introduction / Context: This question is a classic example of a weighted average profit problem. A trader sells parts of the same commodity at different profit percentages, and we are given the overall profit on the total quantity. Such questions test understanding of profit percentage, total cost, total profit, and how to set up and solve linear equations for mixtures of profit rates. Given Data / Assumptions: Total quantity of rice = 630 kg. Part of the rice is sold at 15% profit. The rest is sold at 8% profit. Overall profit on the entire 630 kg is 12%. We assume the cost price per kilogram is uniform. We need to find the quantity sold at 8% profit. Concept / Approach: We can treat this as a weighted average of profit percentages. If the cost price per kilogram is C, then: Profit on the portion sold at 15% is 0.15 C per kg. Profit on the portion sold at 8% is 0.08 C per kg. Overall profit is 0.12 C per kg for all 630 kg. We introduce a variable for the quantity sold at 15% profit, then express the weighted average of profit amounts and equate it to the total profit at 12%. Step-by-Step Solution: Let x be the quantity of rice (in kg) sold at 15% profit. Then the remaining quantity sold at 8% profit is (630 - x) kg. Assume cost price per kg is C (same for all). Total profit from x kg at 15% = 0.15 * C * x. Total profit from (630 - x) kg at 8% = 0.08 * C * (630 - x). Overall profit at 12% on 630 kg = 0.12 * C * 630. Set up the equation: 0.15Cx + 0.08C(630 - x) = 0.12C * 630. Divide both sides by C: 0.15x + 0.08(630 - x) = 0.12 * 630. 0.15x + 50.4 - 0.08x = 75.6. 0.07x = 25.2, so x = 25.2 / 0.07 = 360. Quantity at 8% profit = 630 - 360 = 270 kg. Verification / Alternative check: Check using total profit directly. Suppose C = 1 per kg (for simplicity). Then: 360 kg at 15% gives profit 360 * 0.15 = 54. 270 kg at 8% gives profit 270 * 0.08 = 21.6. Total profit = 54 + 21.6 = 75.6. Total cost = 630 * 1 = 630. Overall profit percent = (75.6 / 630) * 100 = 12%. Everything matches the given condition, so the answer is correct. Why Other Options Are Wrong: If 300 kg were at 8%, the weighted average profit would change and would not equal 12%. Similarly, 280 kg, 260 kg, or 240 kg lead to different average profit percentages once total profit is recomputed, and none match the required 12% overall. Only 270 kg balances the weighted average correctly. Common Pitfalls: A common error is to average 15% and 8% directly to get 11.5% instead of forming an equation based on quantities. Another mistake is confusing which part corresponds to which percentage or making arithmetic errors when solving the equation. Always define the variable clearly, write the total profit expression carefully, and simplify step by step. Final Answer: The trader sells 270 kg of rice at 8% profit.

Question 15

A book seller allows a 10% discount on the printed price of a book and receives a 30% commission from the publisher on that printed price. What percentage profit does the book seller make on the deal?

Accepted Answer

Introduction / Context: This question combines two commercial concepts: trade discount to customers and commission from the publisher. The book seller gets a commission on the printed price but also gives a discount to the buyer. The net effect on profit can be found only by carefully tracking all money flows. Such problems are common in aptitude tests focused on profit and loss and commercial arithmetic. Given Data / Assumptions: Printed price (marked price) of the book is M rupees. Book seller allows 10% discount to the customer, so the customer pays 90% of M. The book seller gets 30% commission from the publisher on M. We assume there are no other costs. We need to find the overall profit percentage of the book seller. Concept / Approach: The idea is: The customer pays selling price SP = 0.9M. The publisher gives commission = 0.3M to the seller. The money which effectively goes from seller to publisher is M - 0.3M = 0.7M, which behaves like cost price for the seller. Effective cost price CP for the seller = 0.7M. Effective selling price SP for the seller = 0.9M (amount collected from customer). Profit percent = ((SP - CP) / CP) * 100. Step-by-Step Solution: Let printed price (marked price) be M. Customer pays 10% less, so SP = 0.9M. Seller gets 30% commission from publisher, that is 0.3M. Amount remitted by seller to publisher = M - 0.3M = 0.7M. This 0.7M is effectively the cost price CP for the seller. Thus CP = 0.7M and SP = 0.9M. Profit = SP - CP = 0.9M - 0.7M = 0.2M. Profit percent = (0.2M / 0.7M) * 100 = (2 / 7) * 100. (2 / 7) * 100 = 28.5714%, which is 28 4/7% approximately. Verification / Alternative check: Take a simple value, for example M = Rs 100. Then: Customer pays RS 90 (10% discount). Publisher allows 30% commission, so seller remits only Rs 70 to publisher. Effective cost price = 70, selling price = 90, profit = 20. Profit percent = (20 / 70) * 100 = 28.5714% = 28 4/7%. This matches the result from algebra. Therefore, the answer is correct. Why Other Options Are Wrong: 20% assumes profit is simply 10% of printed price, ignoring commission. Options 25% and 26 3/7% underestimate the real impact of the commission and discount combined. 18% is even smaller and does not match any logical combination. Only 28 4/7% correctly reflects the net margin after considering both discount and commission. Common Pitfalls: Many learners treat the 30% commission as extra profit without seeing that it also changes the effective cost to the seller. Others use the customer price as cost and get wrong percentages. Always identify who pays what to whom and treat what the seller finally pays out as cost price, and what the seller receives from the customer as selling price. Final Answer: The book seller makes a profit of 28 4/7% on the book.

Question 16

A shopkeeper increases the marked price of an object by 40% above its cost price and then sells it at a discount of 25% on the marked price. If the selling price is Rs 2100, what was the original cost price of the object for the shopkeeper?

Accepted Answer

Introduction / Context: This question combines markup and discount concepts. The shopkeeper first marks the price higher than the cost price and then allows a discount to the customer. The final selling price and these percentages are given, and we are required to work backward to determine the original cost price. This is a typical profit and loss problem used to test percentage handling and equation formation. Given Data / Assumptions: Let the cost price be C rupees. Marked price is 40% above cost price, so marked price = C + 0.4C. Discount offered on marked price = 25%. Final selling price after discount = Rs 2100. We need to find C, the original cost price. Concept / Approach: We use simple percentage relations: Marked price = C * (1 + 40/100) = 1.4C. Selling price = marked price * (1 - 25/100) = 0.75 * marked price. So, selling price SP = 0.75 * 1.4C. We equate this SP to 2100 and solve for C. Step-by-Step Solution: Let cost price be C. Marked price = C + 40% of C = 1.4C. Discount on marked price = 25%, so selling price = 75% of marked price. Therefore SP = 0.75 * 1.4C. SP = 1.05C. Given SP = 2100, so 1.05C = 2100. C = 2100 / 1.05. C = 2000. Thus the original cost price is Rs 2000. Verification / Alternative check: Check using the found cost price: Cost price = 2000. Marked price = 1.4 * 2000 = 2800. Discount = 25% of 2800 = 700. Selling price = 2800 - 700 = 2100. This matches the given selling price exactly. We can also compute the profit: profit = 2100 - 2000 = 100, profit percent = (100 / 2000) * 100 = 5%. Everything is consistent. Why Other Options Are Wrong: If cost price were 3000, marked price and discounted value would not result in 2100. Values like 1500, 1750, and 1800 also fail to produce a final selling price of 2100 when the same 40% markup and 25% discount are applied. Only 2000 satisfies the percentage relations correctly. Common Pitfalls: One common mistake is to add and subtract percentages directly without understanding that they are applied to different bases. Another is treating selling price as cost price while working backward. Always go stepwise from cost price to marked price to selling price and then reverse the process correctly when solving for cost price from a known selling price. Final Answer: The original cost price of the object was Rs 2000.

Question 17

If an article is sold at a loss of 20%, by what fraction must the selling price be multiplied to obtain the cost price of the article?

Accepted Answer

Introduction / Context: This question checks basic understanding of how cost price, selling price, and loss percentage are related. Instead of asking for the percentage directly, it asks for the fraction that converts the selling price back into the cost price when there is a known percentage loss. Such conceptual questions are common in quantitative aptitude sections to ensure students understand percentages as multipliers. Given Data / Assumptions: Loss percentage on the article is 20%. We denote cost price by CP and selling price by SP. Loss percent is defined on cost price. We need a fraction k such that CP = k * SP. Concept / Approach: Use the standard relationships: Loss percent = ((CP - SP) / CP) * 100. 20% loss means SP = 80% of CP. So SP = 0.8 * CP which is also 4/5 of CP. We need CP in terms of SP, so invert the relationship. Thus CP = SP / 0.8 = SP * (5/4). Therefore, the required multiplying fraction is 5/4. Step-by-Step Solution: Let cost price be CP. Loss percent is 20%, so loss = 20% of CP. Therefore SP = CP - 20% of CP. SP = CP - 0.2CP = 0.8CP. Thus SP = (4/5) * CP. We want CP in terms of SP, so CP = SP / (4/5). CP = SP * (5/4). Hence, the selling price must be multiplied by 5/4 to get the cost price. Verification / Alternative check: Assume an easy cost price, for example CP = 100 rupees. A 20% loss means loss = 20 rupees, so SP = 80 rupees. Now, multiply SP by 5/4: SP * (5/4) = 80 * (5/4) = 80 * 1.25 = 100. We get back the original cost price. This confirms that 5/4 is the correct fraction. Any other fraction will not return the cost price from the selling price when the loss is 20%. Why Other Options Are Wrong: 4/5 would reduce the selling price further and cannot give the higher cost price. 8/5 and 6/5 are too large or not consistent with the 20% loss relation. 3/2 equals 1.5 and would correspond to a different percentage relationship. Only 5/4 correctly inverts the 20% loss scenario where SP is 80% of CP. Common Pitfalls: Many learners confuse whether to multiply by (100 - loss%) or divide by it. Some directly assume CP = SP * 0.8, which is the reverse of the correct relation. Always remember: if SP is 80% of CP, then CP must be larger and is obtained by dividing SP by 0.8 or multiplying by 5/4. Final Answer: The selling price must be multiplied by the fraction 5/4 to get the cost price.

Question 18

Ramesh sells a book at a loss of 30%. If he had sold it for Rs 140 more, he would have made a profit of 40%. What is the cost price of the book?

Accepted Answer

Introduction / Context: This problem is a standard profit and loss question where two different selling prices lead to two different percentages, one loss and one profit, on the same article. The difference between these selling prices is given, and we are asked to find the cost price. This type of question tests understanding of percentage profit and loss and the ability to set up a linear equation based on them. Given Data / Assumptions: Ramesh sells the book at a loss of 30%. If he increases the selling price by Rs 140, he earns a profit of 40%. The cost price is the same in both scenarios. We need to find the cost price of the book. Concept / Approach: Let the cost price be C. Then: Selling price at 30% loss = 0.7C. Selling price at 40% profit = 1.4C. The difference between these two selling prices is given as Rs 140. So we form the equation 1.4C - 0.7C = 140 and solve for C. This directly gives us the cost price. Step-by-Step Solution: Let the cost price be C. Selling price at 30% loss = C - 0.3C = 0.7C. Selling price at 40% profit = C + 0.4C = 1.4C. According to the question, the difference between these two selling prices is Rs 140. Therefore, 1.4C - 0.7C = 140. This simplifies to 0.7C = 140. So C = 140 / 0.7 = 200. Thus, the cost price of the book is Rs 200. Verification / Alternative check: Use the cost price C = 200 to verify: Selling price at 30% loss = 0.7 * 200 = 140. Selling price at 40% profit = 1.4 * 200 = 280. Difference between these selling prices = 280 - 140 = 140 rupees, which matches the statement in the question. Thus the calculated cost price is correct. Why Other Options Are Wrong: If C = 280, then 30% loss gives 196 and 40% profit gives 392, difference 196, not 140. With 260, the difference between 0.7 * 260 and 1.4 * 260 is 182. With 300, the difference is 210. With 240, the difference is 168. Therefore, none of these satisfy the condition that the difference between the two selling prices is 140. Common Pitfalls: Students sometimes incorrectly set 30% and 40% on the same selling price or forget that the difference of 140 applies to the selling prices, not the percentages themselves. Another frequent mistake is to add percentages directly or use the wrong base for percentage calculations. Always define cost price as a variable and systematically convert loss and profit percentages into algebraic expressions for the selling prices. Final Answer: The cost price of the book is Rs 200.

Question 19

The profit earned by selling a bucket at an 8% gain is Rs 28 more than the loss incurred when selling it at an 8% loss. What is the cost price (in rupees) of the bucket?

Accepted Answer

Introduction / Context: This is a typical profit and loss question that uses symmetric profit and loss percentages on the same cost price. The difference between the numerical profit and loss amounts is given, and we must determine the cost price. Problems like this reinforce the idea that equal percentage profit and loss on the same cost price lead to equal absolute amounts when expressed in terms of the cost price, and the difference between them relates directly to the cost. Given Data / Assumptions: Gain percentage in one case = 8%. Loss percentage in the other case = 8%. Profit at 8% is larger than the loss at 8% by Rs 28. Let the cost price be C rupees. We need to find the value of C. Concept / Approach: When cost price is C: Profit at 8% is 0.08C. Loss at 8% is also 0.08C. The difference between these profit and loss amounts is 0.08C - ( -0.08C ) or simply 0.16C if we consider the distance between them. However, the question directly states that the profit is Rs 28 more than the loss, which equals 0.16C. So we set 0.16C = 28 and solve. Step-by-Step Solution: Let cost price of the bucket be C. Profit at 8% = 8% of C = 0.08C. Loss at 8% = 8% of C = 0.08C. Difference between profit and loss is 0.08C + 0.08C = 0.16C. Given that this difference equals Rs 28. So 0.16C = 28. C = 28 / 0.16. C = 175. Therefore, the cost price of the bucket is Rs 175. Verification / Alternative check: Check using C = 175: Profit at 8% = 0.08 * 175 = 14. Loss at 8% = 14 as a numerical amount, but it is a reduction. The difference between profit (14) and loss (14) is indeed 14 + 14 = 28 when measured as how much more the profit is than the loss. This matches the given value of 28, so the cost price is verified as correct. Why Other Options Are Wrong: For C = 170, difference = 0.16 * 170 = 27.2, not 28. For C = 190, difference = 30.4. For C = 165, difference = 26.4. For C = 180, difference = 28.8. None of these match the exact difference of 28 stated in the problem. Common Pitfalls: Many students mistakenly take 8% of the selling price instead of 8% of the cost price or forget that the difference between profit and loss at the same rate is effectively 16% of cost price. It is also easy to set up the wrong equation if signs are not handled carefully. Always express profit and loss clearly in terms of cost price and then compute the difference. Final Answer: The cost price of the bucket is Rs 175.

Question 20

The cost of 8 pencils, 5 pens and 3 erasers is Rs 111. The cost of 9 pencils, 6 pens and 5 erasers is Rs 130. The cost of 16 pencils, 11 pens and 3 erasers is Rs 221. What is the total cost (in rupees) of buying 39 pencils, 26 pens and 13 erasers?

Accepted Answer

Introduction / Context: This is a linear equations and arithmetic mixture question framed in a profit and loss or basic arithmetic context. The costs of pencils, pens, and erasers are hidden, but we are given total costs for three different combinations. We must determine the cost of a larger combination of items. The key idea is to treat each item cost as a variable and then either solve the system or cleverly combine equations to reach the required expression directly. Given Data / Assumptions: 8 pencils + 5 pens + 3 erasers cost Rs 111. 9 pencils + 6 pens + 5 erasers cost Rs 130. 16 pencils + 11 pens + 3 erasers cost Rs 221. All pencils have the same cost, all pens have the same cost, and all erasers have the same cost. We need the cost of 39 pencils + 26 pens + 13 erasers. Concept / Approach: Let: Cost of one pencil = P. Cost of one pen = Q. Cost of one eraser = R. We then write three linear equations by comparing coefficients. We could solve for P, Q, and R first, and then calculate the required combination. Another efficient approach is to notice that 39, 26, and 13 are linear combinations of the given sets and derive the cost directly once the unit costs are obtained. Step-by-Step Solution: Let cost of one pencil = P, one pen = Q, and one eraser = R. Equation 1: 8P + 5Q + 3R = 111. Equation 2: 9P + 6Q + 5R = 130. Equation 3: 16P + 11Q + 3R = 221. Solving these three equations simultaneously gives the unit costs. From the system, we obtain P = 10, Q = 5, and R = 2. Now compute the required cost: 39P + 26Q + 13R. 39P = 39 * 10 = 390. 26Q = 26 * 5 = 130. 13R = 13 * 2 = 26. Total cost = 390 + 130 + 26 = 546 rupees. Verification / Alternative check: Verify the unit costs against the original equations: For 8P + 5Q + 3R = 8 * 10 + 5 * 5 + 3 * 2 = 80 + 25 + 6 = 111, correct. For 9P + 6Q + 5R = 90 + 30 + 10 = 130, correct. For 16P + 11Q + 3R = 160 + 55 + 6 = 221, correct. Since the unit costs satisfy all three equations, the computed total of 546 for 39 pencils, 26 pens, and 13 erasers is consistent and correct. Why Other Options Are Wrong: Any other total, such as 316, 624, or 482, would correspond to different unit prices that do not simultaneously satisfy all three original equations. The system of equations has a unique solution, and therefore only one possible total cost is valid. Thus 546 is the only correct choice. Common Pitfalls: Learners may try to guess prices instead of solving the system, leading to random errors. Some might incorrectly subtract or combine equations and obtain wrong values for P, Q, or R. Careful algebraic manipulation or systematic elimination methods are recommended. Always check the values again in all original equations to be certain before using them to calculate the final total cost. Final Answer: The total cost of 39 pencils, 26 pens and 13 erasers is Rs 546.

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