Question 1

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 make 25% profit?

Accepted Answer

Given Selling at Rs. 1920 gives Profit% = Loss% when sold at Rs. 1280. Let cost price be C Profit at 1920 = 1920 − CLoss at 1280 = C − 1280Given: 1920 − C = C − 12802C = 3200 ⇒ C = 1600 Price for 25% profit SP = C(1 + 25%) = 1600 × 1.25 = Rs. 2,000 Final Answer: Sell at Rs. 2,000.

Question 2

If selling price is doubled, the profit triples. Find the profit percent.

Accepted Answer

Let cost price = C and original selling price = S Condition When the selling price is doubled, profit becomes triple: 2S − C = 3(S − C)2S − C = 3S − 3C⇒ 2C = S Original profit Profit = S − C = 2C − C = CProfit% = (C ÷ C) × 100 = 100% Final Answer: Profit percentage = 100%.

Question 3

Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?

Accepted Answer

Given 20 dozens ⇒ 20 × 12 = 240 toys Cost per dozen = Rs. 375 ⇒ Total cost = 20 × 375 = Rs. 7,500 Selling price per toy = Rs. 33 ⇒ Total revenue = 240 × 33 = Rs. 7,920 Compute profit and percent Profit = 7,920 − 7,500 = Rs. 420Profit% = 420 ÷ 7,500 × 100 = 5.60% Final Answer: Percentage profit = 5.60%.

Question 4

Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent is:

Accepted Answer

Per-unit prices Buying: 6 for Rs. 5 ⇒ Cost price (CP) per article = Rs. 5 ÷ 6 Selling: 5 for Rs. 6 ⇒ Selling price (SP) per article = Rs. 6 ÷ 5 Step 1: Gain per article Gain = SP − CP = (6/5) − (5/6) = (36 − 25) ÷ 30 = 11/30 Step 2: Gain percent Gain% = [(Gain) ÷ CP] × 100 = (11/30) ÷ (5/6) × 100= (11/30) × (6/5) × 100 = (66/150) × 100 = 44% Final Answer: Gain percent = 44%.

Question 5

Alfred buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs. 5800, his gain percent is:

Accepted Answer

Given Purchase price = Rs. 4700 Repairs = Rs. 800 Selling price = Rs. 5800 Step 1: Total cost CP = 4700 + 800 = Rs. 5500 Step 2: Profit Profit = SP − CP = 5800 − 5500 = Rs. 300 Step 3: Profit percent Profit% = 300 ÷ 5500 × 100 = 30000 ÷ 5500 ≈ 5.45% Final Answer: Gain percent ≈ 5.45%.

Question 6

100 oranges are bought at the rate of Rs. 350 and sold at the rate of Rs. 48 per dozen. The percentage of profit or loss is:

Accepted Answer

Given Data Total oranges bought = 100 Total cost (cost price, CP) = Rs. 350 Selling rate = Rs. 48 per dozen (12 oranges) Required: overall percentage of profit or loss Step 1: Compute total selling price (SP) Price per orange = 48 ÷ 12 = Rs. 4SP for 100 oranges = 100 × 4 = Rs. 400 Step 2: Compute absolute profit Profit = SP − CP = 400 − 350 = Rs. 50 Step 3: Profit percentage on cost Profit% = (Profit ÷ CP) × 100 = (50 ÷ 350) × 100= 0.142857… × 100 ≈ 14.29% profit Checks & Common Pitfalls Always convert the dozen rate to a per unit price before scaling. Profit% is always computed on cost, not on selling price (unless explicitly asked). Ensure rounding is consistent to two decimals for percentage reporting. Final Answer Overall result is a 14.29% profit.

Question 7

On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is:

Accepted Answer

Given Data Selling 17 balls yields total SP = Rs. 720 Loss equals the cost price of 5 balls Required: cost price (CP) per ball Step 1: Express SP and loss in terms of CP Let CP per ball = Rs. cTotal CP for 17 balls = 17cGiven loss = 5c ⇒ SP = CP − loss = 17c − 5c = 12c Step 2: Equate to the actual SP 12c = 720 ⇒ c = 720 ÷ 12 = Rs. 60 Checks & Common Pitfalls Loss is given as a multiple of CP, not as a percent; model it directly. Do not confuse loss of 5 balls with 5% loss; it is 5 times CP per ball in value. Final Answer Cost price per ball = Rs. 60.

Question 8

When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?

Accepted Answer

Given Data Selling price (with 15% loss) = Rs. 18,700 Required: price to obtain 15% gain Step 1: Recover the cost price (CP) Loss 15% ⇒ SPloss = 0.85 × CP18,700 = 0.85 × CP ⇒ CP = 18,700 ÷ 0.85 = Rs. 22,000 Step 2: Target selling price for 15% gain SPgain = 1.15 × CP = 1.15 × 22,000 = Rs. 25,300 Checks & Common Pitfalls Loss or gain percentages always apply to CP, not to previous SP. Use the reciprocal correctly: dividing by 0.85 to undo a 15% loss. Final Answer Sell the plot for Rs. 25,300 to realize a 15% profit.

Question 9

A shopkeeper sells one transistor for Rs. 840 at a gain of 20% and another for Rs. 960 at a loss of 4%. His total gain or loss percent is:

Accepted Answer

Given Data Transistor 1: SP = Rs. 840 at 20% gain Transistor 2: SP = Rs. 960 at 4% loss Required: net percent gain or loss on both combined Step 1: Compute individual cost prices (CP) For 20% gain: SP = 1.20 × CP ⇒ CP1 = 840 ÷ 1.20 = Rs. 700For 4% loss: SP = 0.96 × CP ⇒ CP2 = 960 ÷ 0.96 = Rs. 1,000 Step 2: Aggregate CP and SP, then find net result Total CP = 700 + 1,000 = Rs. 1,700Total SP = 840 + 960 = Rs. 1,800Net profit = 1,800 − 1,700 = Rs. 100Net profit% = (100 ÷ 1,700) × 100 ≈ 5.88% gain Checks & Common Pitfalls Always evaluate combined profit by summing CPs and SPs, not by averaging percentages. Do not mix up loss base (CP) with SP when reversing loss. Final Answer Overall transaction results in a 5.88% gain.

Question 10

A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?

Accepted Answer

Given Data Purchase rate = 6 toffees for Re. 1 ⇒ CP per toffee = Re. 1 ÷ 6 = Rs. 0.1667 Target: 20% profit on CP Step 1: Compute target SP per toffee SP per toffee = CP × (1 + 20%) = (1/6) × 1.2 = 0.2 = Re. 1 ÷ 5 Step 2: Convert back to a convenient selling phrase If SP per toffee is Re. 0.20, then he must sell 5 for Re. 1. Checks & Common Pitfalls Profit is on cost price; multiply CP by 1.20 for a 20% gain. Do not invert the ratio; ensure the selling pack count decreases when seeking profit. Final Answer He should sell 5 for Re. 1 to gain 20%.

Question 11

A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?

Accepted Answer

Given Data Cost price of cycle = Rs. 1,400 Sold at a loss of 15% Required: selling price (SP) Step 1: Apply loss on CP SP = CP × (1 − 15%) = 1,400 × 0.85 = Rs. 1,190 Checks & Common Pitfalls Loss percent reduces the selling price from CP, not from SP. Keep percentage arithmetic exact to avoid penny errors. Final Answer Selling price = Rs. 1,190.

Question 12

In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?

Accepted Answer

Given Data Original profit = 320% of cost ⇒ Profit = 3.2C if cost = C Original SP = C + 3.2C = 4.2C Then cost increases by 25% (to 1.25C) but SP stays at 4.2C Required: Profit as a % of the (unchanged) SP Step 1: New profit after cost increase New profit = SP − New cost = 4.2C − 1.25C = 2.95C Step 2: Profit as a percentage of SP Profit% on SP = (2.95C ÷ 4.2C) × 100 = (2.95 ÷ 4.2) × 100= 0.702380… × 100 ≈ 70.24% of SP Checks & Common Pitfalls The phrase “percentage of the selling price” changes the base; do not compute on cost. Cancel C to avoid unnecessary numeric assumptions. Round the final percentage to two decimals as requested. Final Answer Profit is approximately 70.24% of the selling price.

Question 13

A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?

Accepted Answer

Given Data Expected profit on cost = 22.5% Total weekly sales (SP) = Rs. 392 Required: profit in rupees Step 1: Relate SP and CP via profit on cost SP = CP × (1 + 22.5%) = 1.225 × CP392 = 1.225 × CP ⇒ CP = 392 ÷ 1.225 = Rs. 320 Step 2: Compute profit Profit = SP − CP = 392 − 320 = Rs. 72 Checks & Common Pitfalls 22.5% on cost means multiply CP by 1.225 to obtain SP. Do not treat 22.5% as on selling price; the base matters. Final Answer Weekly profit = Rs. 72.

Question 14

A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:

Accepted Answer

Given Data Rice 1: 26 kg @ Rs. 20 per kg Rice 2: 30 kg @ Rs. 36 per kg Selling price of mixture = Rs. 30 per kg Required: overall profit percent on cost Step 1: Compute total cost and total quantity Total cost = 26 × 20 + 30 × 36 = 520 + 1080 = Rs. 1,600Total quantity = 26 + 30 = 56 kgAverage cost per kg = 1,600 ÷ 56 = Rs. 28.5714… Step 2: Profit per kg and profit percent Profit per kg = SP − average CP = 30 − 28.5714… = 1.4286…Profit% on cost = (1.4286… ÷ 28.5714…) × 100 = 0.05 × 100 = 5% profit Checks & Common Pitfalls Use weighted average cost; do not average the two prices arithmetically without weights. Ensure per-kg comparison (SP vs average CP) before percentage. Final Answer Overall profit = 5% profit.

Question 15

The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:

Accepted Answer

Given Data Cost price of 20 articles = Selling price of x articles Profit = 25% Required: value of x Step 1: Model CP and SP per article Let CP per article = Rs. cWith 25% profit, SP per article = c × 1.25 Step 2: Set up the equality 20c = x × (1.25c)Cancel c (c > 0): 20 = 1.25x ⇒ x = 20 ÷ 1.25 = 16 Checks & Common Pitfalls Profit increases SP, so fewer articles are needed on the SP side for equality. Do not forget to cancel the common factor c to simplify. Final Answer x = 16.

Question 16

If the cost of 15 eggs is Rs 75, find the total cost of 5 dozen (60) eggs.

Accepted Answer

Introduction: This is a direct unit-rate proportion problem in profit and loss / basic arithmetic pricing. Given Data / Assumptions: 15 eggs cost Rs 75 We want the cost of 5 dozen = 60 eggs Concept / Approach: Compute cost per egg, then multiply by 60. Step-by-Step Solution: Cost per egg = 75 / 15 = Rs 5Total for 60 eggs = 60 * 5 = Rs 300 Verification / Alternative check: Proportionally, if 15 cost 75, then 60 (which is 4 times 15) costs 4 * 75 = 300. Why Other Options Are Wrong: 400, 500, 600: Do not match proportional scaling. Common Pitfalls: Confusing dozen count; forgetting 1 dozen = 12 eggs. Final Answer: 300

Question 17

A stationer buys diaries at Rs 75 per dozen and sells them at Rs 15 per piece. What is the profit in rupees on selling one dozen?

Accepted Answer

Introduction: Compute total selling price per dozen and subtract the cost price per dozen to get profit in rupees. Given Data / Assumptions: Cost price (per dozen) = Rs 75 Selling price per piece = Rs 15 Concept / Approach: There are 12 pieces in a dozen, so SP per dozen = 12 * 15. Profit = SP − CP. Step-by-Step Solution: SP per dozen = 12 * 15 = Rs 180Profit = 180 − 75 = Rs 105 Verification / Alternative check: Profit % (optional) = 105 / 75 * 100 = 140% (not required but validates magnitude). Why Other Options Are Wrong: 75, 100, 110: Do not match the computed difference. Common Pitfalls: Forgetting to convert per-piece SP into per-dozen SP. Final Answer: 105

Question 18

A man buys oranges at 18 for a rupee and sells them at 12 for a rupee. Find the profit percentage.

Accepted Answer

Introduction: Convert both buying and selling conditions to price per orange, then compute profit % using (SP − CP) / CP * 100. Given Data / Assumptions: Buy: 18 for Rs 1 → CP per orange = Rs 1/18 Sell: 12 for Rs 1 → SP per orange = Rs 1/12 Concept / Approach: Profit % = ((1/12 − 1/18) / (1/18)) * 100. Step-by-Step Solution: SP − CP = 1/12 − 1/18 = (3 − 2)/36 = 1/36Profit % = (1/36) / (1/18) * 100 = (18/36) * 100 = 50% Verification / Alternative check: On 36 oranges: CP = 2 rupees, SP = 3 rupees; profit = 1 rupee → 50% of CP. Why Other Options Are Wrong: 33.33%, 66.66%: Result from mis-scaling.None of these, 40%: Do not match calculation. Common Pitfalls: Using per-dozen math directly without converting to unit rates leads to mistakes. Final Answer: 50 %

Question 19

On selling an article for Rs 240, a trader incurs a 4% loss. At what price should he sell to gain 10%?

Accepted Answer

Introduction: We first recover the cost price (CP) from a loss scenario, then compute the selling price (SP) for a desired gain percentage. Given Data / Assumptions: Loss 4% when SP = Rs 240 Want gain 10% Concept / Approach: Loss 4% ⇒ SP = 0.96 * CP ⇒ CP = 240 / 0.96. Then SP_new = 1.10 * CP. Step-by-Step Solution: CP = 240 / 0.96 = 250SP for 10% gain = 1.10 * 250 = Rs 275 Verification / Alternative check: Profit = 275 − 250 = 25; 25/250 * 100 = 10% (as required). Why Other Options Are Wrong: Rs 340, Rs 320, Rs 264: Do not correspond to 10% gain on CP = 250. Common Pitfalls: Applying the percentage to the wrong base (using SP instead of CP). Final Answer: Rs. 275

Question 20

By selling 12 apples for a rupee, a man loses 20%. How many apples per rupee should he sell to gain 20%?

Accepted Answer

Introduction: Convert the given selling rate to unit price, infer cost price, then find the new unit price for 20% gain and turn it back into “how many for a rupee.” Given Data / Assumptions: At 12 for Rs 1, loss = 20% Goal: gain = 20% Concept / Approach: Let SP1 per apple = 1/12. With 20% loss, SP1 = 0.8 * CP ⇒ CP = SP1 / 0.8. For 20% gain, SP2 = 1.2 * CP. Then apples per rupee = 1 / SP2. Step-by-Step Solution: SP1 = 1/12 rupee/appleCP = (1/12) / 0.8 = 1/9.6 rupee/appleSP2 = 1.2 * (1/9.6) = 1/8 rupee/appleApples per rupee = 1 / (1/8) = 8 Verification / Alternative check: Check margins: At 8 for 1 rupee, price is higher than before, aligning with desired gain relative to CP. Why Other Options Are Wrong: 10, 15, 16: Do not satisfy the 20% gain condition given the inferred CP. Common Pitfalls: Mixing up the base for percent gain/loss; forgetting to convert back to items per rupee. Final Answer: 8

Profit and Loss Questions