Question 1

Successive discounts, repair, and resale — A dealer buys an item marked ₹ 25,000 with successive discounts of 20% and 5%, spends ₹ 2000 on repairs, and sells it for ₹ 25,000. What is his overall gain or loss percentage?

Accepted Answer

Introduction / Context: Here we combine successive discounts on the list price, an additional repair outlay, and a final sale price to determine the net percentage result. Successive discounts multiply, not add, and the final profit is compared against the effective cost including repairs. Given Data / Assumptions: List price = ₹ 25,000. Discounts: 20% then 5% ⇒ net multiplier = 0.80 * 0.95. Repair cost = ₹ 2000 (added to purchase cost). Final SP = ₹ 25,000. Concept / Approach: Effective purchase cost = 25,000 * 0.80 * 0.95. Add repairs to get total cost. Profit% = (SP − total cost)/total cost * 100. Step-by-Step Solution: Purchase price = 25000 * 0.80 * 0.95 = 25000 * 0.76 = ₹ 19,000.Total cost = 19,000 + 2,000 = ₹ 21,000.Profit = 25,000 − 21,000 = ₹ 4,000.Profit% = 4000 / 21,000 * 100 ≈ 19.05% gain. Verification / Alternative check: Reverse: 21,000 * 1.1905 ≈ 24,999.5 ≈ 25,000 (rounding explains the small decimal). Why Other Options Are Wrong: The “loss” options contradict positive profit; 25% is too high; 12% gain is too low. Common Pitfalls: Adding discounts (20% + 5% = 25%) instead of compounding (actual 24% off), or forgetting to include the repair cost in the total cost base. Final Answer: 19.05% gain

Question 2

Cost build for a cup of coffee — Coffee powder packet costs ₹ 20 and makes 10 cups. Milk costs ₹ 30 per litre; each cup uses 200 ml. If the seller targets a 25% profit on total cost, what should be the selling price per cup?

Accepted Answer

Introduction / Context: This kitchen arithmetic problem combines a fixed-quantity ingredient (the coffee packet) and a variable ingredient (milk per cup). We compute the total cost for 10 cups, apply the desired profit, and divide by cups to get the per-cup selling price. Given Data / Assumptions: Coffee packet = ₹ 20 and yields 10 cups ⇒ coffee cost per cup = ₹ 2. Milk = ₹ 30/litre = ₹ 0.03/ml. Milk per cup = 200 ml ⇒ milk cost per cup = 200 * 0.03 = ₹ 6. Total cups = 10. Concept / Approach: Total cost for 10 cups = coffee packet cost + milk cost for 10 cups. Apply 25% profit on this total to get required total revenue; then divide by 10. Step-by-Step Solution: Milk for 10 cups = 200 ml * 10 = 2000 ml = 2 litres ⇒ cost = 2 * 30 = ₹ 60.Coffee packet cost = ₹ 20 ⇒ Total cost = 20 + 60 = ₹ 80.Required revenue = 80 * 1.25 = ₹ 100 for 10 cups.SP per cup = 100 / 10 = ₹ 10. Verification / Alternative check: Per cup cost = ₹ 8; adding 25% gives ₹ 10, exactly matching the result. Why Other Options Are Wrong: ₹ 12.50 overshoots 25%; ₹ 6.25 and ₹ 8 ignore profit; ₹ 9.50 underprices the target margin. Common Pitfalls: Forgetting to convert millilitres to litres for milk pricing, or splitting the coffee packet cost incorrectly across cups. Final Answer: ₹ 10

Question 3

Price adjustment scenario — A shopkeeper sells a transistor at 15% above its cost. If instead he had bought it at 5% more than his original cost and also sold it for ₹ 6 more than his original selling price, he would have made 10% profit. What is th…

Accepted Answer

Introduction / Context: This is a two-scenario price puzzle. In the real scenario, the seller gains 15% over cost. In a hypothetical scenario, both the cost and selling price are adjusted, resulting in a 10% profit. We form an equation in the unknown cost price and solve. Given Data / Assumptions: Let original cost = C; original selling price = 1.15C. Alternate scenario: new cost = 1.05C; new selling price = 1.15C + ₹ 6. Alternate profit = 10% ⇒ new SP = 1.10 * new cost. Concept / Approach: Set 1.15C + 6 = 1.10 * (1.05C) and solve for C. This linear equation gives the original cost price directly. Step-by-Step Solution: Equation: 1.15C + 6 = 1.10 * 1.05C = 1.155C.6 = 1.155C − 1.15C = 0.005C.C = 6 / 0.005 = ₹ 1200. Verification / Alternative check: Original SP = 1.15 * 1200 = ₹ 1380. Alternate: cost = 1260; SP = 1386 ⇒ profit = 126 ⇒ 10% of 1260, consistent. Why Other Options Are Wrong: ₹ 800, ₹ 900, ₹ 1000, and ₹ 1400 do not satisfy the equation 1.15C + 6 = 1.155C. Common Pitfalls: Adding or subtracting the percentages instead of multiplying, or forgetting that the alternate 10% is on the new cost. Final Answer: ₹ 1200

Question 4

A merchant has a basket of 80 apples bought for a total cost of ₹240. He wishes to make an overall profit of 20% on the basket. However, he gives one-fourth of the apples (20 apples) to a friend at cost price and sells the remaining 60 apples at a u…

Accepted Answer

Introduction / Context: This question tests combined-profit reasoning: part of the stock is released at cost price (zero profit on that part), while the rest must be priced to deliver the target overall profit on the entire lot. The goal is to compute a per-unit selling price for the remaining apples that compensates for the at-cost giveaway and still yields the stated 20% profit on the full purchase. Given Data / Assumptions: Total apples = 80 Total cost = ₹240 ⇒ cost per apple = ₹240 / 80 = ₹3 Target overall profit = 20% of total cost One-fourth (20 apples) given at cost price Remaining apples to be sold uniformly at price p per apple Concept / Approach: Overall selling value needed for a 20% gain equals total cost * 1.20. Revenue comes from two parts: (i) apples given at cost (no profit but revenue equals their cost), and (ii) apples sold at the decision price p. Sum these to meet the target overall revenue; then solve for p. Step-by-Step Solution: Target revenue = 1.20 * 240 = ₹288Revenue from 20 apples at cost = 20 * ₹3 = ₹60Revenue still required from remaining 60 apples = 288 − 60 = ₹228Thus p = 228 / 60 = ₹3.80 per apple Verification / Alternative check: If p = ₹3.80, revenue on 60 apples = 60 * 3.80 = ₹228; add ₹60 from the cost-price portion to get ₹288. Profit = ₹288 − ₹240 = ₹48, which is exactly 20% of ₹240. Why Other Options Are Wrong: ₹3.00: Yields no profit overall, since everything effectively sells at cost.₹3.60: Overall revenue becomes too low (₹60 + ₹216 = ₹276), giving only a 15% profit.₹4.80: Overshoots; overall profit would exceed 20%. Common Pitfalls: Confusing the required price on the remaining apples with the average price for the entire lot; forgetting that selling part at cost contributes zero profit but still counts toward revenue; miscomputing cost per apple (₹3 here). Final Answer: ₹ 3.80

Question 5

A bookseller sells a book at a gain of 10%. If he had bought it at 4% less and sold it for ₹6 more, he would have gained 18 3/4% (recovered assumption for a consistent solvable stem). What is the cost price (CP) of the book?

Accepted Answer

Introduction / Context: Problems of this type compare two nearby scenarios with small tweaks to cost and selling price, resulting in a different profit percentage. By modeling both cases with variables, one can set up an equation that eliminates the selling price and reveals the true cost price. The original statement had a conflicting percentage; under the Recovery-First Policy, interpreting it as 18 3/4% (i.e., 18.75%) makes the data consistent and solvable. Given Data / Assumptions: Actual sale at 10% gain: SP₁ = 1.10 * CP = 1.10x Alternate case: CP′ = 0.96x (4% less), SP′ = SP₁ + ₹6 Alternate gain% = 18.75% on CP′ ⇒ SP′ = 1.1875 * CP′ Concept / Approach: Equate SP′ from both expressions and solve for x (the original CP). This approach leverages linear relations between cost and selling price and uses percentage conversions accurately. Step-by-Step Solution: SP′ = 1.1875 * (0.96x) = 1.14xBut SP′ = SP₁ + 6 = 1.10x + 6Therefore, 1.10x + 6 = 1.14x ⇒ 6 = 0.04x ⇒ x = ₹150 Verification / Alternative check: At CP = ₹150: actual SP₁ = ₹165 (10% gain). Alternate CP′ = ₹144 and alternate SP′ (1.1875 of 144) = ₹171. SP₁ + 6 = 165 + 6 = 171 — consistent with the scenario. Why Other Options Are Wrong: ₹130/₹140/₹160 do not satisfy the equation 1.10x + 6 = 1.14x under the recovered 18.75% condition. Common Pitfalls: Applying the 4% to selling price instead of cost; reading the percentage as 11 3/4% or 118 3/4% which makes the problem inconsistent; failing to convert 18 3/4% to 0.1875 decimal form accurately. Final Answer: ₹ 150

Question 6

A shopkeeper’s profit P is assumed to be a linear function of transportation charge t and quantity q: P = A*q + B*t (no constant term). He makes ₹10,000 by selling 20 units with t = ₹400, and ₹12,000 by selling 25 units with t = ₹600. Find the linea…

Accepted Answer

Introduction / Context: This is a modeling question in which profit is postulated to depend linearly on two variables: the quantity sold and the transportation charge. With two observed operating points, we can uniquely determine the coefficients of the linear model in the form P = A*q + B*t, assuming no constant term is needed (as directed by the options). Given Data / Assumptions: P( q = 20, t = 400 ) = 10,000 P( q = 25, t = 600 ) = 12,000 Form: P = A*q + B*t Concept / Approach: Set up two linear equations in A and B using the two data points, then solve simultaneously. Because the model omits a constant term, the two unknowns map directly to the slopes with respect to q and t, respectively. Step-by-Step Solution: 20A + 400B = 10,00025A + 600B = 12,000Subtract (first from second): (5A + 200B) = 2,000 ⇒ A + 40B = 400 ⇒ A = 400 − 40BPlug into 20A + 400B = 10,000 ⇒ 20(400 − 40B) + 400B = 10,0008,000 − 800B + 400B = 10,000 ⇒ −400B = 2,000 ⇒ B = −5Then A = 400 − 40(−5) = 400 + 200 = 600Hence P = 600q − 5t Verification / Alternative check: Check point 1: 600*20 − 5*400 = 12,000 − 2,000 = 10,000. Check point 2: 600*25 − 5*600 = 15,000 − 3,000 = 12,000. Both match exactly. Why Other Options Are Wrong: Other coefficient pairs do not satisfy both data points simultaneously; substituting will produce mismatches. Common Pitfalls: Including an unnecessary constant term; arithmetic slip when eliminating variables; forgetting that B can be negative (transport cost reduces profit). Final Answer: 600q - 5t

Question 7

A person sold a table at a profit of 15%. If he had bought it for 25% less and then sold it for ₹60 less than his original selling price, he would have made a profit of 32%. What was the original cost price of the table?

Accepted Answer

Introduction / Context: We are given two linked scenarios: the actual sale (15% gain on the true cost) and a hypothetical case where both the cost and selling price change, producing a different profit percentage. Expressing all prices in terms of the original cost allows us to form one linear equation and solve for the original cost price (CP). Given Data / Assumptions: Original CP = x; original SP = 1.15x Alternate CP′ = 0.75x (25% less) Alternate SP′ = original SP − ₹60 = 1.15x − 60 Alternate profit% = 32% on CP′ ⇒ SP′ = 1.32 * CP′ = 1.32 * 0.75x = 0.99x Concept / Approach: Equate the two expressions for SP′ to eliminate SP′ and obtain a single equation in x. This is a common “what if” profit-and-loss transformation technique. Step-by-Step Solution: 1.15x − 60 = 0.99x0.16x = 60 ⇒ x = 60 / 0.16 = ₹375 Verification / Alternative check: Original sale: SP = 1.15 * 375 = ₹431.25. Alternate: CP′ = 0.75 * 375 = ₹281.25 and SP′ = 431.25 − 60 = ₹371.25; profit% = (371.25 − 281.25)/281.25 * 100 = 32% — consistent. Why Other Options Are Wrong: ₹300/₹350/₹400 do not satisfy the exact 32% condition after the stipulated changes. Common Pitfalls: Applying the 25% reduction to the selling price instead of cost; mixing up which price is reduced by ₹60; rounding too early. Final Answer: ₹ 375

Question 8

Two bicycles together cost ₹1,600. If the first is sold at 10% profit and the second at 20% profit, the seller’s revenue is slightly less than if he had interchanged the profit rates (first at 20%, second at 10%) by ₹5. What is the difference betwee…

Accepted Answer

Introduction / Context: We compare two selling scenarios with the same pair of bicycles but swapped profit rates. Because total cost is fixed, the only change is how profits are distributed across the two items. The difference between the two total revenues directly reveals the difference in their cost prices. Given Data / Assumptions: Let costs be x and y with x + y = 1,600 Scenario 1 revenue: 1.10x + 1.20y Scenario 2 revenue: 1.20x + 1.10y Scenario 2 exceeds Scenario 1 by ₹5 Concept / Approach: Subtract the two expressions to eliminate common terms: (1.20x + 1.10y) − (1.10x + 1.20y) = 0.10x − 0.10y. Set this equal to ₹5 and solve for (x − y). Step-by-Step Solution: 0.10(x − y) = 5x − y = 50Therefore, the difference in cost prices is ₹50 Verification / Alternative check: Let x = 825 and y = 775 (sum 1,600 and difference 50). Scenario 1 SP = 1.10*825 + 1.20*775 = 907.5 + 930 = 1,837.5; Scenario 2 SP = 1.20*825 + 1.10*775 = 990 + 852.5 = 1,842.5; difference = ₹5 — matches. Why Other Options Are Wrong: ₹25/₹40/₹75 do not satisfy the precise ₹5 revenue difference upon swapping profit rates. Common Pitfalls: Attempting to compute individual costs instead of recognizing the neat cancellation; forgetting that only the distribution, not the total cost, changes. Final Answer: ₹ 50

Question 9

A trader mixes 26 kg of rice priced at Rs. 20 per kg with 30 kg of another variety of rice priced at Rs. 36 per kg and sells the entire 56 kg mixture at Rs. 30 per kg. What is his profit percentage on the whole transaction?

Accepted Answer

Introduction / Context: This is a mixture and profit–loss question. A trader mixes two varieties of rice with different cost prices and then sells the mixture at a single uniform selling price per kg. To find the profit percentage, we must first compute the total cost price of the mixture, then the total selling price, and finally express the profit as a percentage of the cost price. Given Data / Assumptions: - First variety: 26 kg at Rs. 20 per kg. - Second variety: 30 kg at Rs. 36 per kg. - Total mixture quantity = 26 kg + 30 kg = 56 kg. - Mixture is sold at Rs. 30 per kg. - All rice is sold, and there are no other expenses or losses. Concept / Approach: Total cost price (CP) of the mixture equals the sum of the costs of each variety. Total selling price (SP) is the selling rate per kg multiplied by the total mass of the mixture. Profit = SP - CP. The profit percentage is then calculated using the formula: profit percent = (profit / CP) * 100. We must carry out these steps carefully to avoid arithmetic mistakes. Step-by-Step Solution: Step 1: Compute cost of first variety: 26 kg at Rs. 20 per kg gives 26 * 20 = Rs. 520.Step 2: Compute cost of second variety: 30 kg at Rs. 36 per kg gives 30 * 36 = Rs. 1080.Step 3: Total cost price (CP) of the mixture = 520 + 1080 = Rs. 1600.Step 4: Total quantity of mixture = 26 + 30 = 56 kg.Step 5: Total selling price (SP) = 56 kg * Rs. 30 per kg = 56 * 30 = Rs. 1680.Step 6: Profit = SP - CP = 1680 - 1600 = Rs. 80.Step 7: Profit percentage = (profit / CP) * 100 = (80 / 1600) * 100.Step 8: Simplify: 80 / 1600 = 1 / 20, so profit percent = (1 / 20) * 100 = 5%. Verification / Alternative check: We can also find the average cost price per kg of the mixture and compare it with the selling price. Average CP per kg = total CP / total quantity = 1600 / 56 = 200 / 7 ≈ Rs. 28.57 per kg. Selling price per kg is Rs. 30. The profit per kg = 30 - 28.57 ≈ Rs. 1.43. Profit percent = (1.43 / 28.57) * 100 ≈ 5%. This confirms our calculation from the direct total CP and SP approach. Why Other Options Are Wrong: If it were no profit, no loss, the selling price would have to match the average cost price of about Rs. 28.57 per kg, which it does not. An 8% or 10% profit would require a larger difference between SP and CP than Rs. 80 on Rs. 1600. The 6% option similarly does not match the ratio 80 / 1600. Only 5% accurately reflects the profit. Common Pitfalls: Some learners incorrectly average the prices 20 and 36 directly without weighting them by the quantities 26 and 30, which is wrong. Others forget to sum total quantities or miscalculate products like 30 * 36. Always calculate total cost first and then divide by total quantity if you use the average price method. Final Answer: The trader makes a profit of 5% on the rice mixture.

Question 10

By selling 45 lemons for Rs. 40, a man incurs a loss of 20%. How many lemons should he sell for Rs. 24 so that he makes a profit of 20% on that transaction?

Accepted Answer

Introduction / Context: This is a profit and loss question involving unit cost and unit selling price. The seller first sells lemons at a loss, giving us information about the cost price per lemon. Using this cost price, we must determine how many lemons he should sell for a fixed total selling price in order to achieve a desired profit percentage. Given Data / Assumptions: - He sells 45 lemons for Rs. 40 at a loss of 20%. - He wants to sell some number of lemons for Rs. 24 and make a profit of 20%. - We assume all lemons are identical with the same cost price per lemon. - There are no other expenses. Concept / Approach: First, we find the selling price per lemon in the loss-making case. Using the loss percentage, we recover the cost price per lemon. Next, we use the desired profit percentage to find the required selling price per lemon in the gain-making case. Finally, we divide the total desired selling amount by this new selling price per lemon to find the number of lemons to be sold. Step-by-Step Solution: Step 1: Selling price (SP) for 45 lemons is Rs. 40, so SP per lemon = 40 / 45 = 8 / 9 rupees.Step 2: He sells at a loss of 20%, which means SP = 80% of cost price (CP).Step 3: So 8 / 9 = 0.8 * CP per lemon.Step 4: Hence CP per lemon = (8 / 9) / 0.8 = (8 / 9) / (4 / 5) = (8 / 9) * (5 / 4) = 40 / 36 = 10 / 9 rupees.Step 5: For the second scenario, he wants a profit of 20%, so SP = 120% of CP = 1.2 * CP.Step 6: SP per lemon for 20% profit = 1.2 * (10 / 9) = (6 / 5) * (10 / 9) = 60 / 45 = 4 / 3 rupees.Step 7: Total SP desired in the second case is Rs. 24, so number of lemons = total SP / SP per lemon = 24 / (4 / 3).Step 8: Simplify: 24 / (4 / 3) = 24 * (3 / 4) = 72 / 4 = 18 lemons. Verification / Alternative check: Confirm using cost and profit. Cost per lemon is 10 / 9 rupees, so cost of 18 lemons = 18 * (10 / 9) = 20 rupees. Selling them for Rs. 24 gives a profit of 24 - 20 = Rs. 4. Profit percent = (4 / 20) * 100 = 20%. This matches the required profit, confirming that 18 lemons is correct. Why Other Options Are Wrong: 16 lemons would cost 16 * (10 / 9) = 160 / 9 ≈ Rs. 17.78, giving a profit larger than 20%. 20 lemons cost 200 / 9 ≈ Rs. 22.22, so the profit would be less than 20% at Rs. 24. 22 and 24 lemons also fail to give exactly 20% profit when you compute cost and compare with Rs. 24. Common Pitfalls: Some learners confuse loss and profit percentages and treat them symmetrically, which is incorrect. Others skip computing cost price per lemon and try to work directly with total amounts, which often leads to mistakes. Always find CP first when both loss and profit scenarios are involved. Final Answer: The man should sell 18 lemons for Rs. 24 to gain 20%.

Question 11

The cost price of 20 identical articles is equal to the selling price of x such articles. If the trader makes a profit of 25% on each article, what is the value of x?

Accepted Answer

Introduction / Context: This profit and loss question relates total cost and total selling price for different numbers of identical articles. The key idea is that if the cost price of 20 articles equals the selling price of x articles, and there is a 25% profit, then the selling price per article is 25% above cost, which allows us to build a simple equation and solve for x. Given Data / Assumptions: - All articles are identical and have the same cost and selling price per unit. - Cost price of 20 articles = selling price of x articles. - Profit percentage on each article = 25%. - We must determine the value of x. Concept / Approach: Let the cost price per article be C. Then the selling price per article is C plus 25% of C, which is 1.25C or 5C / 4. Total cost price for 20 articles is 20C, and total selling price for x articles is x * 5C / 4. Since these two totals are equal, we can set up an equation and solve directly for x. Step-by-Step Solution: Step 1: Let cost price per article = C rupees.Step 2: Profit is 25%, so selling price per article = C + 0.25C = 1.25C = 5C / 4.Step 3: Total cost price of 20 articles = 20C.Step 4: Total selling price of x articles = x * (5C / 4).Step 5: Given that cost price of 20 articles equals selling price of x articles, set 20C = x * (5C / 4).Step 6: Cancel C on both sides (C ≠ 0): 20 = x * (5 / 4).Step 7: Solve for x: x = 20 * (4 / 5) = 80 / 5 = 16.Step 8: Hence, x = 16. Verification / Alternative check: Take a simple value for C to confirm. Suppose C = Rs. 4. Then selling price SP per article = 5C / 4 = 5 rupees. Cost price of 20 articles = 20 * 4 = Rs. 80. We want SP of x articles to also be Rs. 80, so 5x = 80 giving x = 16. This matches our algebraic solution. Why Other Options Are Wrong: Values 15, 18, 20, or 25 all fail when substituted into the relation 20C = x * (5C / 4). For example, if x = 20, then SP for 20 articles would be 20 * 5C / 4 = 25C, which is larger than 20C and does not match the given equality. Only x = 16 balances total cost and total selling price under a 25% profit. Common Pitfalls: Some learners misinterpret the statement and assume that 20 and x refer to numbers in a ratio rather than equality of money values. Others forget that profit is applied on cost price and not on selling price. Always define an algebraic variable for cost price or selling price and build equations carefully. Final Answer: The value of x is 16.

Question 12

If the selling price of an article is doubled, the trader's profit becomes three times the original profit. What is the original profit percentage on the article?

Accepted Answer

Introduction / Context: This is an algebraic profit–loss question involving relationships between cost price, selling price, and profit. You are told how the profit changes when the selling price is doubled, and you must deduce the original profit percentage. This requires careful algebraic setup using variables for cost price and selling price. Given Data / Assumptions: - Let original cost price (CP) of the article be C rupees. - Let original selling price (SP) of the article be S rupees. - Original profit = S - C. - When the selling price is doubled, the new selling price is 2S. - New profit becomes three times the original profit. Concept / Approach: The key step is to convert the statement "If selling price is doubled, the profit triples" into an equation. Original profit is S - C. New profit is 2S - C. According to the question, 2S - C = 3(S - C). Solving this equation gives a relationship between S and C, which we then convert into a profit percentage: profit percent = ((S - C) / C) * 100. Step-by-Step Solution: Step 1: Original profit = S - C.Step 2: After doubling the selling price, new SP = 2S, so new profit = 2S - C.Step 3: Given that the new profit is three times the original profit, we have 2S - C = 3(S - C).Step 4: Expand the right side: 2S - C = 3S - 3C.Step 5: Rearrange terms: bring all to one side: 2S - C - 3S + 3C = 0.Step 6: Simplify: (2S - 3S) + (-C + 3C) = -S + 2C = 0.Step 7: Hence -S + 2C = 0 which gives S = 2C.Step 8: Original profit = S - C = 2C - C = C.Step 9: Profit percentage = (profit / cost price) * 100 = (C / C) * 100 = 100%. Verification / Alternative check: Take a simple numerical example. Let C = Rs. 100. Then S = 2C = Rs. 200. Original profit = 200 - 100 = Rs. 100, which is 100% of cost. After doubling SP, new SP = 2S = Rs. 400. New profit = 400 - 100 = Rs. 300. New profit is exactly three times the original profit (3 * 100 = 300), confirming the algebraic solution and the 100% profit rate. Why Other Options Are Wrong: 200%, 300%, or 400% profit would imply far larger original profits than the condition allows when you double the selling price. For example, if original profit were 200%, then S would be 3C, and doubling S would not lead to only triple profit. 50% profit similarly fails to satisfy the 2S - C = 3(S - C) condition. Only 100% matches the equation derived from the problem. Common Pitfalls: Many students misinterpret the phrase "profit triples" as "profit increases by 300%" or confuse it with tripling of the selling price. Others substitute arbitrary values without setting up a general equation, leading to inconsistent results. Keeping track of cost price, selling price, and profit with clear variables helps avoid these misunderstandings. Final Answer: The original profit percentage on the article is 100%.

Question 13

A shopkeeper cheats to the extent of 10% both while buying and while selling goods by using false weights. What is his overall gain percentage on the transaction?

Accepted Answer

Introduction / Context: This question involves successive gains achieved by cheating on both the buying and selling sides using false weights. The shopkeeper effectively gets more goods than he pays for when buying and gives less goods than he charges for when selling. We assume the market price per true kilogram is the same in both directions, and we compute his net gain based purely on quantity misrepresentation. Given Data / Assumptions: - Market price of the commodity is assumed to be Rs. P per true kg (P is a positive constant). - While buying, he cheats by 10% using false weights to his advantage. - While selling, he again cheats by 10% using false weights to his advantage. - The cheating is purely in terms of weight, not in the quoted price per kilogram. - We must find his overall percentage gain. Concept / Approach: A convenient way is to assume the quoted price per kg remains P for both buying and selling, and then model how much true quantity he receives or gives in each case. A common interpretation is that while buying he uses weights that are 10% heavier (so he receives 1.1 kg of true goods for the price of 1 kg), and while selling he uses weights that are 10% lighter (so he gives only 0.9 kg of true goods while charging for 1 kg). From this we compute his effective cost price and selling price per true kilogram and then calculate the overall profit percentage. Step-by-Step Solution: Step 1: Assume market price per kg = P rupees.Step 2: While buying, he uses a weight 10% heavier than the true kg, that is 1.1 kg, but calls it 1 kg.Step 3: He pays P rupees for what he calls 1 kg, but actually receives 1.1 kg of goods.Step 4: So his effective cost price (CP) per true kg = P / 1.1 = P * (10 / 11).Step 5: While selling, he uses a weight 10% lighter than true, i.e., 0.9 kg, but calls it 1 kg.Step 6: He charges P rupees for what he calls 1 kg, but actually gives only 0.9 kg of goods.Step 7: So his effective selling price (SP) per true kg = P / 0.9 = P * (10 / 9).Step 8: Now compute the profit per true kg: profit = SP - CP = P * (10 / 9) - P * (10 / 11).Step 9: Factor out P * 10: profit = P * 10 * (1 / 9 - 1 / 11) = P * 10 * ((11 - 9) / 99) = P * 10 * (2 / 99) = 20P / 99.Step 10: Effective cost price CP per kg = P * (10 / 11) = 10P / 11.Step 11: Profit percent = (profit / CP) * 100 = (20P / 99) / (10P / 11) * 100.Step 12: Simplify: (20P / 99) * (11 / 10P) * 100 = (220 / 990) * 100 = (22 / 99) * 100 ≈ 22.22%. Verification / Alternative check: Take P = Rs. 11 for easier numbers. Then CP per true kg = 10 rupees and SP per true kg ≈ 12.22 rupees. Profit per kg ≈ 2.22 rupees on a cost of 10 rupees, giving a profit percent of about 22.2%. This numerical check matches the algebraic result. Since the options are in whole percentages, we select the closest value, which is 22%. Why Other Options Are Wrong: 20% is slightly less than the actual approximate 22.22% gain. 21% is also an underestimate. 23% is slightly too high, and 18% is much lower than the derived figure. Only 22% is reasonably close to the true value of about 22.2%, and is the standard answer used in such questions. Common Pitfalls: Some learners treat the 10% cheating as being on price instead of weight and use factors like 0.9P and 1.1P directly, leading to a different result. Others forget to compute the gains per true kilogram and instead mix the quoted and actual quantities incorrectly. Always keep clear which quantity (true kg vs. quoted kg) is used for buying and selling, and then derive effective CP and SP per true unit. Final Answer: The shopkeeper's overall gain on the transaction is approximately 22%.

Question 14

A milkman buys pure milk at Rs. x per litre and sells the mixture at Rs. 2x per litre. He mixes 2 litres of water with every 6 litres of pure milk before selling. Assuming water is free, what percentage profit does he make on his cost price?

Accepted Answer

Introduction / Context: This problem is a classic mixture and profit question that tests understanding of how adding a free component such as water affects overall profit percentage. The key idea is that the seller pays only for milk but charges customers for the entire mixture, including the water, which creates a higher effective selling price per unit of cost. Given Data / Assumptions: Cost price of pure milk = Rs. x per litre. Selling price of the mixture = Rs. 2x per litre. For every batch, 6 litres of milk are mixed with 2 litres of water. Water is assumed to be free, so it has zero cost. We need to find the profit percentage on the cost of the milk used. Concept / Approach: Profit percentage is calculated as (Profit / Cost price) * 100. Here, the cost is only for the milk, while revenue is collected on the total mixture, which includes both milk and water. We first compute the total cost of the milk portion, then compute the total selling price of the mixture for one batch, find the profit amount, and finally convert this profit into a percentage of the cost price. Step-by-Step Solution: Step 1: For each batch, the milkman uses 6 litres of milk and 2 litres of water, so total mixture = 6 + 2 = 8 litres.Step 2: Cost price for 6 litres of milk = 6 * x = 6x rupees. Water adds no cost.Step 3: Selling price of the 8 litres mixture = 8 * 2x = 16x rupees.Step 4: Profit amount = selling price - cost price = 16x - 6x = 10x rupees.Step 5: Profit percentage = (Profit / Cost price) * 100 = (10x / 6x) * 100 = (10 / 6) * 100 = (5 / 3) * 100 = 166.67% approximately. Verification / Alternative check: Assume x = 1 for simplicity. Then cost of 6 litres of milk is Rs. 6, and selling price of 8 litres of mixture is Rs. 16.Profit = 16 - 6 = Rs. 10. Profit percentage = 10 / 6 * 100 ≈ 166.67%.This matches the result from the algebraic method, confirming correctness. Why Other Options Are Wrong: 60% and 100% are too low and would correspond to much smaller markups than doubling the price while adding free water. A profit of 116% ignores the extra 2 litres of water revenue. The value 133.33% comes from mixing ratios other than 6 litres of milk to 2 litres of water. Only 166.67% fits the given data. Common Pitfalls: Many learners mistakenly treat the total 8 litres as if all were purchased at cost, which underestimates profit. Others compute profit on the selling price instead of cost price, or they ignore that water is free. Carefully distinguishing between what is paid for and what is sold is critical in all mixture-based profit questions. Final Answer: The milkman's profit percentage on his cost is approximately 166.67%.

Question 15

Books are bought at prices ranging from Rs. 200 to Rs. 350 and sold at prices ranging from Rs. 300 to Rs. 425. What is the greatest possible total profit that can be made by selling eight books?

Accepted Answer

Introduction / Context: This question is about maximizing profit when both cost prices and selling prices vary within given ranges. It checks understanding of how to choose the most favourable combination of minimum costs and maximum selling prices to get the greatest possible profit when buying and selling multiple items. Given Data / Assumptions: Cost prices of individual books lie between Rs. 200 and Rs. 350. Selling prices of individual books lie between Rs. 300 and Rs. 425. Exactly eight books are bought and sold. We are asked for the greatest possible total profit, assuming the trader can choose any allowed prices within the given ranges. Concept / Approach: Profit on each book is selling price minus cost price. To maximize total profit, each book should be bought as cheaply as possible and sold as expensively as possible, within the allowed ranges. Therefore, we use the lowest possible cost price and the highest possible selling price for every book and then multiply the resulting profit per book by the total number of books, which is eight. Step-by-Step Solution: Step 1: Minimum allowable cost price per book = Rs. 200.Step 2: Maximum allowable selling price per book = Rs. 425.Step 3: Maximum profit per book = 425 - 200 = Rs. 225.Step 4: Number of books sold = 8.Step 5: Maximum total profit = profit per book * number of books = 225 * 8 = Rs. 1800. Verification / Alternative check: Consider one book: if it is bought at Rs. 350 (the highest cost) and sold at Rs. 300 (the lowest selling price), there would be a loss.However, the problem asks for the greatest possible profit, so we always pair the minimum cost with the maximum selling price.Using Rs. 225 profit per book and eight books again leads to Rs. 1800, confirming the calculation. Why Other Options Are Wrong: Rs. 600 and Rs. 1200 assume lower per-book profits, which would come from less favourable price combinations. Rs. 1500 is still below the maximum possible Rs. 1800 and corresponds to a lower effective gain per book. The option “None of these” is incorrect because Rs. 1800 is achievable using the extreme points in the allowed ranges. Common Pitfalls: Students sometimes average the cost and selling price ranges and calculate profit based on average values, which does not give the maximum possible profit. Others mistakenly think that each book must be bought at different prices, whereas the question allows every book to be bought at the minimum and sold at the maximum price. For “greatest possible” style questions, always consider the extreme favourable values within the given constraints. Final Answer: The greatest possible total profit on eight books is Rs. 1800.

Question 16

The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to earn a profit of 25% on its cost price?

Accepted Answer

Introduction / Context: This profit and loss question uses a symmetric condition where the percentage profit at one selling price equals the percentage loss at another selling price. From this condition we can determine the cost price and then compute a new selling price that yields a specified profit percentage. It tests both algebraic manipulation and understanding of the relationship between cost, selling price, profit and loss. Given Data / Assumptions: Selling price 1 (with profit) = Rs. 1920. Selling price 2 (with loss) = Rs. 1280. The percentage profit at Rs. 1920 equals the percentage loss at Rs. 1280. The cost price of the article is the same in both cases. We must find the selling price that gives a 25% profit. Concept / Approach: Let the cost price be C. Profit percentage at Rs. 1920 is (1920 - C) / C * 100, and loss percentage at Rs. 1280 is (C - 1280) / C * 100. These percentages are equal, so the numerators must be equal: 1920 - C = C - 1280. Solving this equation gives C. Once C is known, a 25% profit means new selling price = C * 1.25. This approach neatly uses symmetry around cost price. Step-by-Step Solution: Step 1: Let C be the cost price of the article.Step 2: Profit at Rs. 1920: profit amount = 1920 - C.Step 3: Loss at Rs. 1280: loss amount = C - 1280.Step 4: Given that profit percentage equals loss percentage, we set 1920 - C = C - 1280.Step 5: Solve: 1920 + 1280 = 2C which gives 3200 = 2C, so C = 1600.Step 6: For a 25% profit, required selling price = C * 1.25 = 1600 * 1.25 = Rs. 2000. Verification / Alternative check: Check profit at Rs. 1920: profit = 1920 - 1600 = 320, so profit percentage = 320 / 1600 * 100 = 20%.Check loss at Rs. 1280: loss = 1600 - 1280 = 320, so loss percentage = 320 / 1600 * 100 = 20%.Thus the given condition is satisfied. A 25% profit on cost price 1600 is 400, so selling price 1600 + 400 = Rs. 2000, matching the calculation. Why Other Options Are Wrong: Rs. 2200 and Rs. 2400 correspond to profit percentages larger than 25% on a cost of Rs. 1600. The option “Data inadequate” is incorrect because the symmetric condition uniquely determines the cost price. Rs. 2600 would represent a much higher profit percentage and is not asked for in the question. Common Pitfalls: Learners sometimes mistakenly equate profit percentage to loss amount or mix up the formula for percentage. Others forget that equality of percentages implies equality of profit and loss amounts only because the denominator (cost price) is the same in both cases. Writing the expressions explicitly and simplifying step by step avoids such confusion. Final Answer: To earn a 25% profit, the article should be sold for Rs. 2000.

Question 17

The cost price of 12 pens is equal to the selling price of 8 pens of the same type. What is the percentage gain made on each pen?

Accepted Answer

Introduction / Context: This is a standard profit percentage question where a relationship between the cost price and selling price for different quantities is given. The problem checks whether you can convert that quantity relationship into a ratio of selling price to cost price for a single unit and then compute the gain percentage for each item. Given Data / Assumptions: Cost price of 12 pens equals selling price of 8 pens. All pens are identical in type and quality. The trader buys and sells at uniform prices per pen. We must determine the percentage gain on each pen. Concept / Approach: Let cost price per pen be C and selling price per pen be S. Then total cost for 12 pens is 12C and total selling price for 8 pens is 8S. The statement that these are equal gives an equation 12C = 8S. From this equation we find the ratio S / C, which directly tells us by what factor the selling price exceeds the cost price. Profit percentage is then (S - C) / C * 100. Step-by-Step Solution: Step 1: Let cost price per pen be C and selling price per pen be S.Step 2: Given that 12C = 8S.Step 3: Simplify the equation: divide both sides by 4 to get 3C = 2S.Step 4: Rearranging, S = 3C / 2 = 1.5C.Step 5: Profit per pen = S - C = 1.5C - C = 0.5C.Step 6: Profit percentage = (Profit / Cost price) * 100 = (0.5C / C) * 100 = 50%. Verification / Alternative check: Assume C = Rs. 2 per pen. Then S = 1.5 * 2 = Rs. 3 per pen.Total cost of 12 pens = 12 * 2 = Rs. 24. Total selling price of 8 pens = 8 * 3 = Rs. 24, which matches the given condition.Profit per pen = 3 - 2 = Rs. 1, so profit percentage = 1 / 2 * 100 = 50%. Why Other Options Are Wrong: Gains of 12% or 30% imply that S is only slightly greater than C, which contradicts the ratio 12C = 8S. A gain of 60% would require S = 1.6C, not 1.5C, and 25% gain would mean S = 1.25C, again inconsistent with the condition. Only a 50% gain matches the derived ratio S = 1.5C. Common Pitfalls: Some learners misinterpret the equality of total cost and total selling price as applying to a single pen instead of to different quantities. Others incorrectly take ratios like 12:8 as cost to selling price directly without introducing unit cost symbols. Setting up the equation carefully with C and S is the most reliable method to avoid these mistakes. Final Answer: The gain made on each pen is 50% of the cost price.

Question 18

Tarun receives a 30% discount on the labelled (marked) price of an article and buys it at this reduced price. He then sells the article for Rs. 8750, making a profit of 25% on his purchase price. What was the original labelled price of the article?

Accepted Answer

Introduction / Context: This question combines discount and profit concepts. Tarun buys an article after getting a concession on the labelled price and then sells it at a profit over his actual cost. The task is to work backwards from his final selling price and known profit percentage to recover the labelled price. This is a typical exam question involving reverse percentage calculations. Given Data / Assumptions: Labelled price of the article = L rupees (unknown). Tarun gets a discount of 30% on L. So his purchase price = 70% of L. He sells the article for Rs. 8750. His profit on the purchase price is 25%. We must find the value of L, the original labelled price. Concept / Approach: First, we interpret the 25% profit as selling price = 1.25 times the purchase price. Because the purchase price itself is 70% of the labelled price, or 0.7L, the selling price can be expressed in terms of L as 1.25 * 0.7L. This expression is set equal to the actual selling price of Rs. 8750. Solving this equation yields L directly. This approach avoids unnecessary intermediate steps. Step-by-Step Solution: Step 1: Purchase price after 30% discount = 70% of L = 0.7L.Step 2: Tarun makes a profit of 25% on this purchase price.Step 3: Therefore, selling price = 1.25 * 0.7L = 0.875L.Step 4: We are told the selling price equals Rs. 8750, so 0.875L = 8750.Step 5: Solve for L: L = 8750 / 0.875.Step 6: Note that 0.875 = 7 / 8, so L = 8750 * 8 / 7 = Rs. 10000. Verification / Alternative check: If L = Rs. 10000, the discount of 30% leads to a purchase price of 0.7 * 10000 = Rs. 7000.A 25% profit on Rs. 7000 is 0.25 * 7000 = Rs. 1750.So the selling price becomes 7000 + 1750 = Rs. 8750, exactly matching the given value. Why Other Options Are Wrong: Labelled prices such as Rs. 12000, Rs. 13000, or Rs. 14000 would lead to purchase and selling prices different from Rs. 8750 when the same discount and profit percentages are applied. Rs. 9000 also fails the check because 70% of 9000 is 6300 and 25% profit on that would not reach 8750. Only Rs. 10000 satisfies all conditions. Common Pitfalls: Students often apply the 25% profit directly to the labelled price instead of to the discounted price, which is incorrect. Others may mis-handle the division by 0.875, or convert percentages incorrectly. Writing the relationships clearly as equations and reducing fractions like 0.875 to 7 / 8 helps to avoid computational mistakes. Final Answer: The original labelled price of the article was Rs. 10000.

Question 19

Due to a reduction of 25% in the price of oranges, a customer can now purchase 4 more oranges for Rs. 16 than before. What was the original price of one orange?

Accepted Answer

Introduction / Context: This question uses the idea that when a price falls by a certain percentage, the same amount of money can buy more units of the item. It connects percentage change in price with change in quantity purchased and requires setting up an equation involving the original price per unit. It is a common style in quantitative aptitude sections on discounts and unitary method. Given Data / Assumptions: Original price per orange = p rupees (unknown). Price is reduced by 25%, so new price per orange = 75% of p. A customer spends Rs. 16 both before and after the reduction. After the reduction, the customer can buy 4 more oranges for Rs. 16. We must find the original value of p. Concept / Approach: Let the number of oranges bought before the reduction be n. Then n = 16 / p. After a 25% reduction, the new price is 0.75p, so the new number of oranges is 16 / (0.75p). The difference in quantities is given as 4. We set up an equation representing this difference and solve for p. Working symbolically first keeps the algebra structured and less error-prone. Step-by-Step Solution: Step 1: Original price per orange = p. New price after 25% reduction = 0.75p.Step 2: Number of oranges before reduction = 16 / p.Step 3: Number of oranges after reduction = 16 / (0.75p) = 16 / (3p / 4) = (16 * 4) / (3p) = 64 / (3p).Step 4: The customer gets 4 more oranges after the price reduction, so 64 / (3p) - 16 / p = 4.Step 5: Compute the left side: 64 / (3p) - 16 / p = (64 - 48) / (3p) = 16 / (3p).Step 6: So 16 / (3p) = 4, which gives 16 = 12p, so p = 16 / 12 = 4 / 3 ≈ Rs. 1.33. Verification / Alternative check: If p = 4 / 3, original price per orange ≈ Rs. 1.33, so original quantity = 16 / (4 / 3) = 16 * 3 / 4 = 12 oranges.New price = 75% of 4 / 3 = 3 / 4 * 4 / 3 = 1 rupee per orange, so new quantity = 16 / 1 = 16 oranges.Difference in quantities = 16 - 12 = 4 oranges, which matches the question. Why Other Options Are Wrong: A price of Rs. 1 would lead to 16 oranges both before and after, giving no difference. Prices such as Rs. 1.50 or Rs. 1.60 do not produce a difference of exactly 4 when you redo the calculations. Rs. 0.80 is also inconsistent with both the percentage reduction and the fixed expenditure of Rs. 16. Only Rs. 1.33 (4 / 3) per orange fits all the conditions. Common Pitfalls: Many learners forget to express both original and new quantities explicitly, or they mis-handle the 25% reduction by subtracting 0.25 rupees instead of 25% of p. Another common mistake is to take the difference as 4 rupees instead of 4 oranges. Paying attention to units and carefully distinguishing between price and quantity prevents these errors. Final Answer: The original price of one orange was approximately Rs. 1.33 (that is, Rs. 4 / 3).

Question 20

A man buys some oranges at Rs. 5 per dozen and an equal number of oranges at Rs. 4 per dozen. He then sells all of the oranges at Rs. 5.50 per dozen and makes a profit of Rs. 50 in total. How many oranges does he buy?

Accepted Answer

Introduction / Context: This problem combines weighted average cost and total profit to determine the number of items bought. The shopkeeper buys oranges at two different rates and sells all of them at a single selling price per dozen. The goal is to compute how many dozens, and hence how many oranges, he must have bought to achieve a stated profit. Given Data / Assumptions: Some oranges are bought at Rs. 5 per dozen. An equal number of oranges are bought at Rs. 4 per dozen. All oranges are sold at Rs. 5.50 per dozen. Total profit earned = Rs. 50. We are asked how many oranges he buys, which is usually expressed in dozens first. Concept / Approach: Let the man buy n dozens at Rs. 5 per dozen and another n dozens at Rs. 4 per dozen. Then the total quantity is 2n dozens. We calculate total cost price, total selling price, and hence total profit in terms of n. Equating that profit to Rs. 50 allows us to solve for n. Finally we can express the answer either as dozens or individual oranges. Step-by-Step Solution: Step 1: Let number of dozens bought at Rs. 5 per dozen be n. Then the same number n dozens are bought at Rs. 4 per dozen.Step 2: Total cost price = 5n + 4n = 9n rupees.Step 3: Total quantity of oranges = 2n dozens.Step 4: Selling price per dozen = Rs. 5.50, so total selling price = 2n * 5.5 = 11n rupees.Step 5: Total profit = selling price - cost price = 11n - 9n = 2n rupees.Step 6: Given that total profit is Rs. 50, so 2n = 50 which implies n = 25 dozens at each rate.Step 7: Therefore total dozens bought = 2n = 50 dozens. Verification / Alternative check: If he buys 25 dozens at Rs. 5 and 25 dozens at Rs. 4, cost = 25 * 5 + 25 * 4 = 125 + 100 = Rs. 225.He sells 50 dozens at Rs. 5.50, so sales revenue = 50 * 5.5 = Rs. 275.Profit = 275 - 225 = Rs. 50, exactly as given in the question. Why Other Options Are Wrong: 30, 40 or 60 dozens would produce total profits different from Rs. 50 when the same calculation is repeated. For example, 40 dozens total would give 2n = profit = 40 rupees, not Rs. 50. The option 20 dozens corresponds to n = 10, giving profit 20 rupees only. Only 50 dozens satisfies the profit condition. Common Pitfalls: Some learners treat the phrase “equal number” as equal cost instead of equal quantity. Others incorrectly divide the Rs. 50 profit by Rs. 5.50 directly without considering the mixed purchase prices. Introducing a variable n and writing separate expressions for cost and revenue is the most systematic and reliable approach. Final Answer: The man buys a total of 50 dozens of oranges.

Profit and Loss Questions