# Problems on Profit Loss

Q11. A person sells an article for Rs. 11 and gains as much percent as the cost price of the article in rupees. The cost price of the article is

(a) 10

(b) 9

(c) 8

(d) 7

**Answer:** (a) 10

Let the C.P be Rs. x

∴ Gain = x%

∴ S.P = x + x X (x/100)

⇒ 11 = | 100x + x^{2} |

100 |

⇒ 100x + x^{2} = 1100

⇒ x^{2} + 100x - 1100 = 0

⇒ x^{2} + 110x - 10x - 1100 = 0

⇒ x(x + 110) - 10(x + 110) = 0

⇒ (x + 110) (x - 10) = 0

∴ x + 110 = 0 or x - 10 = 0

⇒ x = - 110 ⇒ x = 10

∴ C.P = Rs. 10

Q12. By selling a tape-recorder for Rs. 760, I lose 5%. What percent shall I gain by selling it for Rs. 1000 ?

(a) 10%

(b) 20%

(c) 22%

(d) 25%

**Answer:** (d) 25%

Let, the C.P be Rs. x

S.P = Rs. 760

Loss = 5%

Now, x - x X | 5 | = 760 |

100 |

⇒ x - | x | = 760 |

20 |

⇒ | 19x | = 760 |

20 |

⇒ x = (760 X 20)/19

⇒ x = 40 X 20 = 800

∴ C.P = Rs. 800

New S.P = Rs. 1000

∴ Gain = Rs. (1000 - 800) = Rs. 200

∴ Gain% = (200/800) X 100 = 25%

Q13. A shopkeeper sells a pair of sunglasses at a profit of 25%. If he had bought it at 25% less and sold it for Rs. 10 less, then he would have gained 40%. The cost price of the pair of sunglasses is

(a) Rs. 30

(b) Rs. 50

(c) Rs. 60

(d) Rs. 70

**Answer:** (b) Rs. 50

Let, the C.P be Rs. x

S.P = Rs. (125/100)x = Rs. (5x/4)

New C.P = Rs. (75/100) X x = Rs. 3x/4

New S.P = Rs. ( | 5x | - 10) |

4 |

∴ ( | 5x | - 10) = | 140 | X | 3x | = | 21x |

4 | 100 | 4 | 20 |

⇒ | 5x | - | 21x | = 10 |

4 | 20 |

⇒ 4x = 200

⇒ x = 50

∴ C.P = Rs. 50

Q14. On a Rs. 20,000 payment order a person has choice between three successive discounts of 20%, 20% and 10% and three successive discounts of 40%, 5% and 5% . By choosing the better one, he can save

(a) Rs. 690

(b) Rs. 710

(c) Rs. 725

(d) Rs. 785

**Answer:** (a) Rs. 690

1st payment = 80% of 80% of 90% of Rs. 20,000

= ( | 80 | X | 80 | X | 90 | X 20000) |

100 | 100 | 100 |

= Rs. 11520

2nd Payment = 60% of 95% of 95% of 20000

= Rs. ( | 60 | X | 95 | X | 95 | X 20000) |

100 | 100 | 100 |

=Rs. 10830

By choosing the better one he can save

Rs. (11520 - 10830) = Rs. 690

Q15. Successive discounts of 5% and 10% are equivalent to a single discount of

(a) 12.3%

(b) 14.5%

(c) 15.3%

(d) 15.9%

**Answer:** (b) 14.5%

Let the C.P be Rs. 100

Now S.P = 95% of 90% of Rs. 100

= (95/100) X (90/100) X 100

= Rs. 85.50

∴ Single discount = (100 - 85.50) % = 14.5%

Q16. A single discount equivalent to successive discounts of 40%, 30% and 10% is

(a) 43.5%

(b) 51.5%

(c) 55.8%

(d) 62.2%

**Answer:** (d) 62.2%

Let the C.P be Rs. x

∴ S.P = Rs. 60% of 70% of 90% of 100

= Rs. (60/100) X (70/100) X (90/100) X 100

= Rs. 37.8

∴ Single discount = (100 - 37.8) % = 62.2 %

Q17. The marked price of an electric iron is Rs. 450. The shopkeeper allows a discount of 10% and gains 8%. If no discount is allowed, his gain percent would be

(a) 10%

(b) 20%

(c) 25%

(d) 30%

**Answer:** (b) 20%

S.P = 90% of Rs. 450

= (90/100) X 450 = Rs. 405

Gain = 8%

∴ C.P = Rs. (100/108 X 405) = Rs. 375

New C.P = Rs. 375

New S.P = Rs. 450

∴ Gain = Rs. (450 - 375) = Rs. 75

∴ Gain % = (75/375) X 100 = 20%

Q18. A shopkeeper marks his goods to gain 30% . But he allows 10% discount for cash payment. His profit percent is

(a) 14%

(b) 17%

(c) 21%

(d) 25%

**Answer:** (b) 17%

Let the C.P be Rs. 100

Then M.P = Rs. 100 + 30 = Rs. 130

S.P = 90% of Rs. 130

= (90/100) X 130 = Rs. 117

∴ Profit = Rs. (117 - 100) = Rs. 17

∴ Profit % = (17/100) X 100 = 17%

Q19. A pen is listed for Rs. 12. A discount of 15% is given on it. A second discount is given bringing the price down to Rs. 8.16. The rate of second discount is

(a) 10%

(b) 16%

(c) 20%

(d) 28%

**Answer:** (c) 20%

Let the second discount be x%, then

100 - x | X | 85 | X 12 = 8.16 |

100 | 100 |

⇒ 51 (100 - x) = 4080

⇒ 51x = 5100 - 4080 = 1020

⇒ x = 20

∴ Second discount = 20%

Q20. A fan is listed at Rs. 1400 and a discount of 20% is offered on the list price. What additional discount must be offered to the customer to bring the net price of Rs. 1100

(a) 1(11/14)%

(b) 2(11/14)%

(c) 1(13/14)%

(d) 2(13/14)%

**Answer:** (a) 1(11/14)%

Listed Price = Rs. 1400

S.P = 1400 X (80/100) = Rs. 1120

New S.P = Rs. 1100

∴ Discount = Rs. (1120 - 1100) = Rs. 20

Discount % = (20/1120) X 100 = 1(11/14) %