Profit and Loss problems
- 1. If an article is sold at a gain of 6% instead of at a loss of 6% then the seller gets Rs. 6 more. The C.P. of the article is?
Options- A. Rs. 50
- B. Rs. 94
- C. Rs. 100
- D. Rs. 106 Discuss
Correct Answer: Rs. 50
Explanation:
? 6% of C.P. + 6% of C.P. = Rs. 6
? 12% of C.P. = Rs. 6
? 12 / 100 x CP = 6
? CP = (100 x 6) / 12 = 50
? C.P. = Rs. 50
- 2. A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs. 55 more. he would have had a profit of 40%. The C.P. of the article is?
Options- A. Rs. 200
- B. Rs. 225
- C. Rs. 250
- D. None of these Discuss
Correct Answer: Rs. 250
Explanation:
Let C.P. = Rs. P
Then S.P. = Rs. (90/100) x P = Rs. (9 x P)/10
New C.P. = Rs. (80/100) x P = Rs. (4 x P)/5
Now, Gain = 40%
? New S.P. Rs. (140/100 x 4P/5) = Rs. 28P/25
? 28P/25 - 9P/10 = Rs. 250
- 3. A dealer sells a radio at a gain of 10%. If he had bought it at 10% less and sold it for Rs. 132 less, he would have still gained 10%. The C.P. of the radio is?
Options- A. Rs. 1188
- B. Rs. 1200
- C. Rs. 1320
- D. None of these Discuss
Correct Answer: Rs. 1200
Explanation:
Let C.P. = P
Then S.P. = Rs. (110/100 x P) = Rs. 11P/10
New C.P. = Rs. (90/100 x P ) = Rs. 9P/10
New S.P. = (110/100 x 9P) / 100
? 11P/10 - 99P/100 = 132
? P = 1200
? C.P. = Rs. 1200
- 4. Due to an increase of 30% in the price of eggs, 3 eggs less are available for Rs. 7.80. The present rate of eggs per dozen is?
Options- A. Rs. 8.64
- B. Rs. 8.88
- C. Rs. 9.36
- D. None of these Discuss
Correct Answer: Rs. 9.36
Explanation:
Let the original rate be 'P' paise per egg.
Number of eggs bought for Rs. 7.80 = 780/P
New rate = (130% of P) paise per egg = 13P/10 paise per egg
Number of eggs bought for Rs. 7.80 = 780 x 10/13P = 600/P
? 780/P - 600/P = 3
? 3P = 180
? P = 60
So, present rate = (13 x 60)/10 paise per egg = 78 paise per egg
= Rs. 9.36 per dozen
- 5. A man sells two horses for Rs, 4000 each, neither losing nor gaining in the deal. If he sold one horse at a gain of 25% the other horse is sold at a loss of?
Options- A. 162/3%
- B. 182/9%
- C. 25%
- D. None of these Discuss
Correct Answer: 162/3%
Explanation:
C.P. of two horses = Rs. 8000
S.P. of one horse = Rs. 4000
Gain = 25%
? C.P. of this horse = Rs (100/125) x 4000 = Rs.3200
C.P. of another horse = Rs. (8000 - 3200) = Rs. 4800
S.P. of this horse = Rs. 4000
? Loss% = (800/4800) x 100 % = 162/3%
- 6. A grocer sells rice at a profit of 10% and uses weight which are 20% less than the market weight. The total gain earned by him will be?
Options- A. 30%
- B. 35%
- C. 37.5%
- D. None of these Discuss
Correct Answer: 37.5%
Explanation:
Let us consider a packet of rice marked 1 kg
Then its actual weight = (80% of 1 kg) = 0.8 kg
Let C.P. of 1 kg be Rs. 100
Then C.P. of 0.8 kg = Rs. 0.8 x 100 = Rs. 80
Now, S.P of 1 kg = 110% of C.P.of 1 kg = Rs. 110
? Gain = (1.1 - 0.8) x 100 = 0.3 x 100 = 130
? Required gain% = [0.3/ (0.8 x 130)] x 100)%
= 37. 5%
- 7. A bicycle is sold at a gain of 16%. If it had been sold for Rs. 20 more, 20% would have been gained. The C.P. of the bicycle is?
Options- A. Rs. 350
- B. Rs. 400
- C. Rs. 500
- D. Rs. 600 Discuss
Correct Answer: Rs. 500
Explanation:
? (20% of C.P.) - (16% of C.P.) = Rs. 20
? 4% of C.P. = 20
? (4/100 x C.P.) = 20
? C.P. = Rs. (100 x 20/4)
? C.P. of the bicycle = Rs. 500
- 8. A radio dealer sold radio at a loss of 2.5%. Had he sold it for Rs. 100 more, he would have gained 7 1/ 2 %. In order to gain 12 1/ 2 % he should sell it for?
Options- A. Rs. 850
- B. Rs. 925
- C. Rs. 1080
- D. Rs. 1125 Discuss
Correct Answer: Rs. 1125
Explanation:
It is clear that (2.5% of C.P. + 7.5% of C.P.) = 100
? C.P. = Rs. 1000
Now, gain = 121/2
So, Required S.P. = 1121/2% of C.P.
= Rs. (225 / 200) x 1000
= Rs. 1125
- 9. A man sells an article at a gain of 15%. If he had bought it at 10% less and sold it for Rs. 4 less, he would have gained 25%. The C.P. of the article is?
Options- A. Rs. 140
- B. Rs. 150
- C. Rs. 160
- D. Rs. 180 Discuss
Correct Answer: Rs. 160
Explanation:
? (115% of C.P.) - (125% of 90% of C.P.) = 4
? [115/100 - (125 x 90) / (100 x 100)] x CP = 4
? C.P. = Rs. 160
- 10. 6% more is gained by selling a radio for Rs. 475 than by selling for Rs. 451. The C.P. of the radio is?
Options- A. Rs. 400
- B. Rs. 434
- C. Rs. 440.50
- D. None of these Discuss
Correct Answer: Rs. 400
Explanation:
Difference between two selling prices = 475 - 451 = Rs. 24
? 6% of C.P. = Rs. 24
Hence, C.P. = Rs. (24 x 100 / 6) = Rs. 400
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