Profit and Loss problems
- 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?
Options- A. Rs. 2000
- B. Rs. 2200
- C. Rs. 2400
- D. Data inadequate Discuss
Correct Answer: Rs. 2000
Explanation:
Let C.P. be Rs. x.
| Then, | 1920 - x | x 100 = | x - 1280 | x 100 |
| x | x |
⟹ 1920 - x = x - 1280
⟹ 2x = 3200
⟹ x = 1600
| ∴ Required S.P. = 125% of Rs. 1600 = Rs. | ❨ | 125 | x 1600 | ❩ | = Rs 2000. |
| 100 |
- 2. If selling price is doubled, the profit triples. Find the profit percent.
Options- A. 66 2⁄3
- B. 100
- C. 105 1⁄3
- D. 120 Discuss
Correct Answer: 100
Explanation:
Let C.P. be Rs. x and S.P. be Rs. y.
Then, 3(y - x) = (2y - x) ⟹ y = 2x.
Profit = Rs. (y - x) = Rs. (2x - x) = Rs. x.
| ∴ Profit % = | ❨ | x | x 100 | ❩% = 100% |
| x |
- 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?
Options- A. 3.5
- B. 4.5
- C. 5.6
- D. 6.5 Discuss
Correct Answer: 5.6
Explanation:
| Cost Price of 1 toy = Rs. | ❨ | 375 | ❩ | = Rs. 31.25 |
| 12 |
Selling Price of 1 toy = Rs. 33
So, Gain = Rs. (33 - 31.25) = Rs. 1.75
| ∴ Profit % = | ❨ | 1.75 | x 100 | ❩% | = | 28 | % = 5.6% |
| 31.25 | 5 |
- 4. Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent is:
Options- A. 30%
- B. 331⁄3%
- C. 35%
- D. 44% Discuss
Correct Answer: 44%
Explanation:
Suppose, number of articles bought = L.C.M. of 6 and 5 = 30.
| C.P. of 30 articles = Rs. | ❨ | 5 | x 30 | ❩ | = Rs. 25. |
| 6 |
| S.P. of 30 articles = Rs. | ❨ | 6 | x 30 | ❩ | = Rs. 36. |
| 5 |
| ∴ Gain % = | ❨ | 11 | x 100 | ❩% = 44%. |
| 25 |
- 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:
Options- A. 4 4⁄7%
- B. 5 5⁄11%
- C. 10%
- D. 12% Discuss
Correct Answer: 5 5⁄11%
Explanation:
Cost Price (C.P.) = Rs. (4700 + 800) = Rs. 5500.
Selling Price (S.P.) = Rs. 5800.
Gain = (S.P.) - (C.P.) = Rs.(5800 - 5500) = Rs. 300.
| Gain % = | ❨ | 300 | x 100 | ❩% | = 5 | 5 | % |
| 5500 | 11 |
- 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:
Options- A. 14 2⁄7% gain
- B. 15% gain
- C. 14 2⁄7% loss
- D. 15 % loss Discuss
Correct Answer: 14 2⁄7% gain
Explanation:
| C.P. of 1 orange = Rs. | ❨ | 350 | ❩ | = Rs. 3.50 |
| 100 |
| S.P. of 1 orange = Rs. | ❨ | 48 | ❩ | = Rs. 4 |
| 12 |
| ∴ Gain% = | ❨ | 0.50 | x 100 | ❩% | = | 100 | % = 14 | 2 | % |
| 3.50 | 7 | 7 |
- 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:
Options- A. Rs. 45
- B. Rs. 50
- C. Rs. 55
- D. Rs. 60 Discuss
Correct Answer: Rs. 60
Explanation:
(C.P. of 17 balls) - (S.P. of 17 balls) = (C.P. of 5 balls)
⟹ C.P. of 12 balls = S.P. of 17 balls = Rs.720.
| ⟹ C.P. of 1 ball = Rs. | ❨ | 720 | ❩ | = Rs. 60. |
| 12 |
- 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%?
Options- A. Rs. 21,000
- B. Rs. 22,500
- C. Rs. 25,300
- D. Rs. 25,800 Discuss
Correct Answer: Rs. 25,300
Explanation:
85 : 18700 = 115 : x
| ⟹ x = | ❨ | 18700 x 115 | ❩ | = 25300. |
| 85 |
Hence, S.P. = Rs. 25,300.
- 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:
Options- A. 5 15⁄17 % loss
- B. 5 15⁄17 % gain
- C. 6 2⁄3 % gain
- D. None of these Discuss
Correct Answer: 5 15⁄17 % gain
Explanation:
| C.P. of 1st transistor = Rs. | ❨ | 100 | x 840 | ❩ | = Rs. 700. |
| 120 |
| C.P. of 2nd transistor = Rs. | ❨ | 100 | x 960 | ❩ | = Rs. 1000 |
| 96 |
So, total C.P. = Rs. (700 + 1000) = Rs. 1700.
Total S.P. = Rs. (840 + 960) = Rs. 1800.
| ∴ Gain % = | ❨ | 100 | x 100 | ❩% | = 5 | 15 | % |
| 1700 | 17 |
- 10. A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?
Options- A. 3
- B. 4
- C. 5
- D. 6 Discuss
Correct Answer: 5
Explanation:
C.P. of 6 toffees = Re. 1
| S.P. of 6 toffees = 120% of Re. 1 = Rs. | 6 |
| 5 |
| For Rs. | 6 | , toffees sold = 6. |
| 5 |
| For Re. 1, toffees sold = | ❨ | 6 x | 5 | ❩ | = 5. |
| 6 |
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