# Problems on Profit Loss

Q1. A chair is bought for Rs. 450 and sold at Rs. 740. Find the gain percent

(a) 17 | 1 | % |

7 |

(b) 25 | 1 | % |

3 |

(c) 43 | 1 | % |

7 |

(d) 64 | 4 | % |

9 |

**Answer:**

(d) 64 | 4 | % |

9 |

Here C.P = Rs. 450 and S.P = Rs. 740

∴ Gain = Rs. (740 - 450) = Rs. 290

∴ Gain % = | 290 | X 100% | = 64 | 4 | % |

450 | 9 |

Q2. If a man were to sell his chair for Rs. 620, he would loss 20%. To gain 25%, he should sell it for

(a) 873.77

(b) 968.75

(c) 1010.55

(d) 1123.36

**Answer:** (b) 968.75

Let the C.P of the chair be Rs. x

S.P = Rs. 620

Loss = 20%

A/Q, x - | 20x | = 620 |

100 |

⇒ x - | x | = 620 |

5 |

⇒ | 4x | = 620 |

5 |

⇒ x = | 620 X 5 | = 775 |

4 |

∴ C.P = Rs. 775

To gain 25%,

C.P = Rs. 775

∴ S.P = Rs. (775 + 775 X (25/100))

= Rs. (775 + 193.75)

=Rs. 968.75

Q3. A man sell his type writer at 5% loss. If he sells it for Rs. 80 more, he gains 5%. The cost price of the typewriter is

(a) 800

(b) 830

(c) 870

(d) 890

**Answer:** (a) 800

Let the cost price be Rs. x

∴ | 105 | X x - | 95 | X x = 80 |

100 | 100 |

⇒ | 21x | - | 19x | = 80 |

20 | 20 |

⇒ 21x - 19x = 1600

⇒ 2x = 1600

⇒ x = 800

∴ C.P = Rs. 800

Q4. Amit sold a bag for Rs. 540, lossing 10%. The cost price of the bag is

(a) 400

(b) 550

(c) 600

(d) 850

**Answer:** (c) 600

Let the cost price be Rs. x

S.P = Rs. 540

Loss % = 10%

Now x - x X | 10 | = 540 |

100 |

⇒ | 10x -x | = 540 |

10 |

⇒ 9x = 5400

⇒ x = 600

∴ C.P = rs. 600

Q5. A bookseller sells a book at a gain of 10%. If he had bought it at 5% less and sold it for Rs. 5 more, he would have gained 18¾ %. The cost price of the book is

(a) 112.35

(b) 120.50

(c) 133.33

(d) 149.80

**Answer:** (c) 133.33

Let the cost price of the book is Rs. x

∴ S.P = x + x X | 10 | = | 110x | = Rs. | 11x |

100 | 100 | 10 |

New C.P = 95% of x = x X | 95 | = | 19x |

100 | 20 |

New S.P = Rs. ( | 11x | + 5 ) |

10 |

Now S.P - C.P = x X 18 | 3 | % |

4 |

⇒ | 11x | + 5 - | 19x | = x X | 75 |

10 | 20 | 4 X 100 |

⇒ | 22x + 100 - 19x | = | 75x |

20 | 400 |

⇒ 3x + 100 = | 75x | X 20 |

400 |

⇒ 12x + 400 = 15x

⇒ 3x = 400

⇒ x = 133.33

∴ C.P = Rs. 133.33

Q6. Hari bought 1200 eggs at Rs. 4 per dozen. He sold 900 of them at 2 for Rs. 1 and the remaining at 5 for Rs. 2. His gain percent is

(a) 35.3 %

(b) 42.5 %

(c) 49.3 %

(d) 56.8 %

**Answer:** (b) 42.5 %

C.P = Rs. ( | 1200 | X 4 ) = Rs. 400 |

12 |

S.P = Rs. ( | 900 | + | 2 X 300 | ) = Rs. (450 + 120) = Rs. 570 |

2 | 5 |

∴ Gain = Rs. (570 - 400) = Rs. 170

Gain% = | 170 | X 100 | = 42.5 % |

400 |

Q7. A merchant has 1000 kg of Rice, part of which sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% is

(a) 350 Kg

(b) 420 Kg

(c) 540 Kg

(d) 600 Kg

**Answer:** (d) 600 Kg

Let the C.P of 1 kg Rice be Rs. x

∴ C.P of 1000 Kg Rice = Rs. 1000x

Let the Rice sold at 8% gain be y Kg

Then the Rice sold at 18% gain = (1000 - y) Kg

∴ ( | 108 | X xy) + [ | 118 | X x (1000 - y)] = | 114 | X 1000x |

100 | 100 | 100 |

⇒ | 27y | + | 59 (1000 - y) | = 1140 |

25 | 50 |

⇒ 54y + 59(1000 - y) = 57000

⇒ 5y = 2000

⇒ y = 400

∴ Required quantity = (1000 - 400)kg = 600 kg

Q8. A radio is sold for Rs. 880 at a profit of 10%. What would have been the gain or loss percent, had it been sold for Rs. 780 ?

(a) 2½ %

(b) 3¼ %

(c) 3½ %

(d) 5¾ %

**Answer:** (a) 2½ %

Let, the C.P be Rs. x

S.P = Rs. 880

Profit% = 10%

Now, x + x X (10/100) = 880

⇒ x + x/10 = 880

⇒ 11x/10 = 880

⇒ x = (880 X 10)/11 = 800

∴ C.P = Rs. 800

New S.P = Rs. 780

∴ Loss = Rs. (800 - 780) = Rs. 20

∴ Loss % = (20/800) X 100 = 2½ %

Q9. A man sold an article at a loss of 10%. If he sells the article for Rs. 10 more he would have gained 5%. The cost price of the article is

(a) Rs. 30

(b) Rs. 36.50

(c) Rs. 54.76

(d) Rs. 66.66

**Answer:** (d) Rs. 66.66

Let the C.P be Rs. x

Loss = 10%

∴ S.P = x - (10x/100) = x - (x/10) = Rs. 9x/10

New S.P = Rs. ( | 9x | + 10) = Rs. | 9x + 100 |

10 | 10 |

Now | 9x + 100 | - x = x X | 5 |

10 | 100 |

⇒ | 9x + 100 - 10x | = | x |

10 | 20 |

⇒ -x + 100 = x/2

⇒ x/2 + x = 100

⇒ 3x/2 = 100

⇒ x = 200/3 = 66.66

∴ C.P = Rs. 66.66

Q10. Mangoes are bought at 5 for Rs. 20 and sold at 6 for Rs. 30. His gain percent is

(a) 18%

(b) 21%

(c) 25%

(d) 28%

**Answer:** (c) 25%

C.P = Rs. 20/5 = Rs. 4 for one mango

S.P = Rs. 30/6 = Rs. 5 for one mango

∴ Gain = Rs (5 - 4) = Rs. 1

Gain% = (1/4) X 100% = 25 %