CBSE Class 10 Mathematics Profit, Loss and Discount MCQs Set 13

Multiple Choice Questions (MCQs) for Class 10 Mathematics: Profit, Loss and Discount

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Practice Profit, Loss and Discount MCQs for Class 10 Mathematics

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Multiple Choice Questions

Question 1: I gain 70 paise on Rs. 70. My gain percent is
(a) 0.1%
(b) 1%
(c) 7%
(d) 10%
Show Answer & Explanation

Answer: (b) 1%

Explanation:
1. Gain = Rs. 0.70 on a cost of Rs. 70
2. Gain % = 0.70/70 × 100 = 1%.

Teacher's Note:
1. Gain percent is always taken on the cost price.
2. Convert paise to rupees before dividing.

Question 2: A shopkeeper sold an article for Rs. 2090.42. Approximately, what will be the percentage profit if he had sold that article for Rs. 2602.58?
(a) 15%
(b) 20%
(c) 25%
(d) 30%
Show Answer & Explanation

Answer: (c) 25%

Explanation:
1. Treat Rs. 2090.42 as the cost price
2. Profit = 2602.58 − 2090.42 = Rs. 512.16
3. Profit % = 512.16/2090.42 × 100 ≈ 24.5%, which is approximately 25%.

Teacher's Note:
1. Use the cost price as the base.
2. Round at the end.

Question 3: Jacob bought a scooter for a certain sum of money. He spent 10% of the cost on repairs and sold the scooter for a profit of Rs. 1100. How much did he spend on repairs if he made a profit of 20%?
(a) Rs. 400
(b) Rs. 440
(c) Rs. 500
(d) Rs. 550
Show Answer & Explanation

Answer: (c) Rs. 500

Explanation:
1. Let the cost be x; repairs = 0.1x, so the total cost = 1.1x
2. Profit = 20% of 1.1x = 0.22x = 1100, so x = 5000
3. Repairs = 10% of 5000 = Rs. 500.

Teacher's Note:
1. Profit is calculated on the total cost including repairs.

Question 4: A property dealer sells a house for Rs. 6,30,000 and in the bargain makes a profit of 5%. Had he sold it for Rs. 5,00,000, what percentage of loss or gain would he have made?
(a) 2 1/4% gain
(b) 10% loss
(c) 12 1/2% loss
(d) 16 2/3% loss
Show Answer & Explanation

Answer: (d) 16 2/3% loss

Explanation:
1. Cost price = 630000 × 100/105 = Rs. 600000
2. At Rs. 500000 the loss = 100000
3. Loss % = 100000/600000 × 100 = 16 2/3%.

Teacher's Note:
1. First find the cost price from the given profit.

Question 5: The ratio of the cost price and the selling price is 4 : 5. The profit percent is
(a) 10%
(b) 20%
(c) 25%
(d) 30%
Show Answer & Explanation

Answer: (c) 25%

Explanation:
1. Let CP = 4k and SP = 5k, so profit = k
2. Profit % = k/4k × 100 = 25%.

Teacher's Note:
1. Take the ratio terms as multiples of k.

Question 6: The profit earned by selling an article for Rs. 900 is double the loss incurred when the same article is sold for Rs. 450. At what price should the article be sold to make a 25% profit?
(a) Rs. 600
(b) Rs. 750
(c) Rs. 800
(d) Data inadequate
Show Answer & Explanation

Answer: (b) Rs. 750

Explanation:
1. Let the cost price be C: 900 − C = 2(C − 450)
2. 900 − C = 2C − 900, so C = 600
3. SP for 25% profit = 600 × 1.25 = Rs. 750.

Teacher's Note:
1. Form an equation from the profit and the loss.

Question 7: If the cost price of 12 pens is equal to the selling price of 8 pens, the gain percent is
(a) 25%
(b) 33 1/3%
(c) 50%
(d) 66 2/3%
Show Answer & Explanation

Answer: (c) 50%

Explanation:
1. 12 × CP = 8 × SP, so SP = 1.5 CP
2. Gain = 50%.

Teacher's Note:
1. Compare the price of one pen in both cases.

Question 8: A man sold 18 cots for Rs. 16800, gaining thereby the cost price of 3 cots. The cost price of a cot is
(a) Rs. 650
(b) Rs. 700
(c) Rs. 750
(d) Rs. 800
Show Answer & Explanation

Answer: (d) Rs. 800

Explanation:
1. SP of 18 cots = cost of 18 cots + cost of 3 cots = cost of 21 cots
2. 16800 = 21 × CP, so CP = Rs. 800.

Teacher's Note:
1. The gain equals the cost of 3 cots.

Question 9: A man buys 2 dozen bananas at Rs. 16 per dozen. After selling 18 bananas at the rate of Rs. 12 per dozen, the shopkeeper reduced the rate to Rs. 4 per dozen. The percent loss is
(a) 25.2%
(b) 32.4%
(c) 36.5%
(d) 37.5%
Show Answer & Explanation

Answer: (d) 37.5%

Explanation:
1. Cost = 2 × 16 = Rs. 32
2. 18 bananas at Rs. 12 per dozen = 1.5 × 12 = Rs. 18
3. Remaining 6 bananas at Rs. 4 per dozen = 0.5 × 4 = Rs. 2
4. Total SP = Rs. 20, loss = 12, loss % = 12/32 × 100 = 37.5%.

Teacher's Note:
1. Convert the number of bananas into dozens.

Question 10: By selling 12 toffees for a rupee, a man loses 20%. How many toffees for a rupee should he sell to get a gain of 20%?
(a) 5
(b) 8
(c) 10
(d) 15
Show Answer & Explanation

Answer: (b) 8

Explanation:
1. SP per toffee = 1/12 = 0.8 CP, so CP = 1/9.6 rupee
2. For 20% gain, SP = 1.2/9.6 = 1/8 rupee per toffee
3. He should sell 8 toffees for a rupee.

Teacher's Note:
1. Find the cost of one toffee first.

Question 11: Arun purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of Rs. 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should he sell the mixture to make 30% profit?
(a) Rs. 14.80
(b) Rs. 15.40
(c) Rs. 16.38
(d) Rs. 18.20
Show Answer & Explanation

Answer: (c) Rs. 16.38

Explanation:
1. Total cost = 30 × 11.50 + 20 × 14.25 = 345 + 285 = Rs. 630 for 50 kg
2. CP per kg = 12.60
3. SP per kg = 12.60 × 1.3 = Rs. 16.38.

Teacher's Note:
1. Find the average cost of the mixture first.

Question 12: A shopkeeper professes to sell his goods at cost price but uses a weight of 800 gm instead of a kilogram weight. Thus, he makes a profit of
(a) 20%
(b) 16 2/3%
(c) 25%
(d) None of these
Show Answer & Explanation

Answer: (c) 25%

Explanation:
1. He gives 800 g for the price of 1000 g
2. Gain = 200 g on a cost of 800 g, so profit = 200/800 × 100 = 25%.

Teacher's Note:
1. The cost is that of the goods actually given.

Question 13: A house worth Rs. 1,50,000 is sold by X to Y at 5% profit. Y sells the house back to X at 2% loss. Then, in the entire transaction
(a) X loses Rs. 1350
(b) X gains Rs. 3150
(c) X loses Rs. 4350
(d) X gains Rs. 4350
Show Answer & Explanation

Answer: (b) X gains Rs. 3150

Explanation:
1. X sells to Y for 150000 × 1.05 = Rs. 157500
2. Y sells back for 157500 × 0.98 = Rs. 154350
3. X received 157500 and paid 154350, so X gains Rs. 3150.

Teacher's Note:
1. Track the money received and paid by X.

Question 14: If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 340, the cost of the article is
(a) Rs. 50
(b) Rs. 160
(c) Rs. 200
(d) Rs. 225
Show Answer & Explanation

Answer: (c) Rs. 200

Explanation:
1. The extra gain is 350 − 340 = Rs. 10
2. This is 5% of the cost, so the cost = 10 × 100/5 = Rs. 200.

Teacher's Note:
1. The extra rupees correspond to the extra percentage.

Question 15: The difference between the cost price and the sale price of an article is Rs. 240. If the profit is 20%, the selling price is
(a) Rs. 1240
(b) Rs. 1400
(c) Rs. 1600
(d) Rs. 1440
Show Answer & Explanation

Answer: (d) Rs. 1440

Explanation:
1. Profit = 240 = 20% of CP, so CP = Rs. 1200
2. SP = 1200 + 240 = Rs. 1440.

Teacher's Note:
1. Profit % is on the cost price.

Question 16: A businessman sold 2/3 of his stock at a gain of 20% and the rest at a gain of 14%. The overall percentage of gain to the businessman is
(a) 12%
(b) 17%
(c) 18%
(d) 20%
Show Answer & Explanation

Answer: (c) 18%

Explanation:
1. Overall gain = 2/3 × 20 + 1/3 × 14 = 13 1/3 + 4 2/3 = 18%.

Teacher's Note:
1. Weight each gain percent by the fraction of stock.

Question 17: Two-thirds of a consignment was sold at a profit of 5% and the remainder at a loss of 2%. If the total profit was Rs. 400, the value of the consignment (in Rs.) was
(a) 10,000
(b) 12,000
(c) 15,000
(d) 20,000
Show Answer & Explanation

Answer: (c) 15,000

Explanation:
1. Let the value be V: profit = 2V/3 × 0.05 − V/3 × 0.02 = V(0.1 − 0.02)/3 = 0.08V/3
2. 0.08V/3 = 400, so V = 15000.

Teacher's Note:
1. The loss on the remainder reduces the profit.

Question 18: An article was sold for Rs. y after giving a discount of x%. Then its list price is
(a) 100y/(100 − x)
(b) 100y/(1 − x)
(c) 100y/(1 − x/100)
(d) None of these
Show Answer & Explanation

Answer: (a) 100y/(100 − x)

Explanation:
1. SP = list price × (100 − x)/100
2. List price = 100y/(100 − x).

Teacher's Note:
1. Discount is on the list price.

Question 19: Find the selling price of an article if a shopkeeper allows two successive discounts of 5% each on the marked price of Rs. 80.
(a) Rs. 70.10
(b) Rs. 70.20
(c) Rs. 72
(d) Rs. 72.20
Show Answer & Explanation

Answer: (d) Rs. 72.20

Explanation:
1. SP = 80 × 0.95 × 0.95 = 80 × 0.9025 = Rs. 72.20.

Teacher's Note:
1. Successive discounts multiply and are not simply added.

Question 20: A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price to the printed price of the book is
(a) 45 : 56
(b) 50 : 61
(c) 55 : 69
(d) 99 : 125
Show Answer & Explanation

Answer: (a) 45 : 56

Explanation:
1. SP = 0.9 × printed price = 1.12 × CP
2. CP : printed price = 0.9 : 1.12 = 90 : 112 = 45 : 56.

Teacher's Note:
1. Express the SP in two ways.

Question 21: 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
(a) Rs. 45
(b) Rs. 50
(c) Rs. 55
(d) Rs. 60
Show Answer & Explanation

Answer: (d) Rs. 60

Explanation:
1. Loss = 5 × CP, so SP of 17 balls = 17 CP − 5 CP = 12 CP
2. 12 CP = 720, so CP = Rs. 60.

Teacher's Note:
1. SP = CP − loss.

Question 22: A dealer purchases 22 pencils for Rs. 20 and sells them at the rate of 10 pencils for Rs. 11. His profit percent is
(a) 10%
(b) 20%
(c) 21%
(d) 22%
Show Answer & Explanation

Answer: (c) 21%

Explanation:
1. CP per pencil = 20/22 and SP per pencil = 1.1
2. Profit % = (1.1 − 20/22)/(20/22) × 100 = (1.21 − 1) × 100 = 21%.

Teacher's Note:
1. Compare the price of one pencil in each case.

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Multiple Choice Questions (MCQs) for Class 10 Mathematics Profit, Loss and Discount

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