Profit and Loss problems
- 1. The profit earned after selling a pair of shoes for ? 2033 is the same as the loss incurred after selling the same pair of shoes for ? 1063. What is the cost price of the shoes?
Options- A. ? 1650
- B. ? 1548
- C. ? 1532
- D. Cannot be determined Discuss
Correct Answer: ? 1548
Explanation:
Let the cost price of the shoes = ? x
According to the question,
2033 - x = x - 1063
? 2x = 2033 + 1063 = 3096
? x = 3096/2 = ? 1548
- 2. A man sells an article at a profit of 40%. If he had bought it at 40% less and sold for ? 5 less, he would have gained 50% . Find the cost price of the article .
Options- A. ? 10
- B. ? 15
- C. ? 20
- D. ? 30 Discuss
Correct Answer: ? 10
Explanation:
Let CP = ? 100, then SP = 140
New CP = ? 60 and new SP = (60 x 150)/100 ? 90
According to the question,
?(140 - 90) = ? 50 is equivalent to ? 5.
? ? 100 is equivalent to ? 10.
? CP = ? 10
- 3. A person sold his watch for ? 75 and got a percentage profit equal to the cost price. The cost price of the watch is.
Options- A. ? 40
- B. ? 45
- C. ? 50
- D. ? 55 Discuss
Correct Answer: ? 50
Explanation:
Let CP of the watch be ? N.
Then , According to the question,
[(75 - N)/ N] x 100 = N
? (75 - N) x 100 = N2
? N2 + 100N - 7500 = 0
? N2 + 150N - 50N - 7500 = 0
? N(N + 150) - 50 (N + 150) = 0
? (N + 150) (N - 50) = 0
? N = ? 50
- 4. Two lots of onions with equal quantity, one costing ? 10 per kg and the other costing ? 15 per kg, are mixed together and whole lot is sold at ? 15 per kg. What is the profit or loss?
Options- A. 10% loss
- B. 10% profit
- C. 20% profit
- D. 20% loss Discuss
Correct Answer: 20% profit
Explanation:
Let each lot of onion-contain N kg onion,
Then total cost price of these two lots together = 10N + 15N = 25N
Selling price of whole lot = 15 x (N + N) = 15 x 2N = 30N
Profit percentage = [(30N - 25N)/25N] x 100 %
= (5/25) x 100%
= 20%
- 5. A vender sells lemons at the rate of 5 for ? 14. gaining thereby 40%. For how much did he buy a dozen lemon?
Options- A. ? 20
- B. ? 21
- C. ? 24
- D. ? 28 Discuss
Correct Answer: ? 24
Explanation:
SP of 1 lemon = ? 14/5
Let CP of 1 lemon = N
According to the question, (N x 140)/100 = 14/5
? N = ? 2
? CP for 12 lemons = 12 x 2 = 24
- 6. By selling 32 orange for ? 30 a man loses 25%. How many oranges should be sold for ? 24 so as to gain 20% in the transaction?
Options- A. 16
- B. 24
- C. 32
- D. 28 Discuss
Correct Answer: 24
Explanation:
Let the cost price be ? N.
SP of 1 orange = ? 30/32 = ? 15/16
According to the question, 75N/100 = 15/16
? N = [(15 x 100)/75] x 16 = ? 5/4
SP of 1 orange with 20% profit = ? [(5/4) x 120]/100 = ? 3/2
? In ? 3/2, the number of oranges sold = 1
? in ? 24, the number of oranges sold = (2/3) x 24 = 16
- 7. Kamlesh purchased 120 reams of paper at ? 100 per ream and the expenditure on transport was ? 480. He had to pay an octroi duty of 50 paise per ream and the coolie charges were ? 60. What should he charge per ream to gain 40%?
Options- A. ?155
- B. ? 147
- C. ? 138
- D. ? 165 Discuss
Correct Answer: ? 147
Explanation:
Total cost price = ? (120 x 100) = ? 12000
Total expenditure = 480 + (1/2) x 120 + 60 = ? 600
Total cost price = 12000 + 600 = ? 126000
Gain = 40%
SP of 120 reams = 12600 x (140/100) = ? 17640
? SP per ream = 17640/120 = ? 147
- 8. A producer of a tea blends two varieties of tea from tea gardens one costing ? 18 per kg and another ? 20 kg in the ratio 5 : 3. If he sells the blended variety at ? 21 per kg, then his gain percentage is
Options- A. 18
- B. 8
- C. 10
- D. 12 Discuss
Correct Answer: 12
Explanation:
Let quantities of two types of tea costing ? 18 per kg and ? 20 per kg be 5W kg and 3W kg. respectively.
Then, CP of tea = (18 x 5W) + (20 x 3W)
= 90W + 60W = 150W
SP of tea = 21 x 8W = 168W
Profit percent = [(168W - 150W) / 150W] x 100%
= (18/150) x 100% = 12%
- 9. Pens are bought at 5 for ? 4 and sold at 4 for ? 5. Find the gain per cent.
Options- A. 55%
- B. 45.26%
- C. 56.26%
- D. 60% Discuss
Correct Answer: 56.26%
Explanation:
Let the number of pens bought = 5 x 4 = 20
Then, CP = (4/5) x 20 = ? 16
and SP = (5/4) x 20 = ? 25
? Gain = 25 - 16 = ? 9
Gain % = (9/16) x 100% = 56.25%
- 10. A person purchased 11 articles for ? 10 and sells at 10 articles for ? 11. Find the gain percentage.
Options- A. 22
- B. 20
- C. 1
- D. 21 Discuss
Correct Answer: 21
Explanation:
Cost price of 11 Articles = 10
Cost price of 1 Article = 10/11
and SP of 10 Articles = 11
? SP of 1 Article = 11/10
Now, gain = (11/10) - (10//11)
= (121 - 100)/110 = 21/110
And gain% = [(21/110) / (10/11)] x 100
= (21 x 11)/11 = 21
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