# Problems on Profit Loss

Q61. Mangoes are bought at 4 for Rs. 20 and sold at 3 for Rs. 18. Find the gain percent.

(a) 17%

(b) 20%

(c) 22%

(d) 25%

**Answer:** (b) 20%

C.P of 1 mango = Rs. ^{20}/_{4} = Rs. 5

S.P of 1 mango = Rs. ^{18}/_{3} = Rs. 6

∴ Gain = S.P - C.P = 6 - 5 = Rs. 1

∴ Gain % = ^{1}/_{5} X 100% = 20%

Q62. A lamp marked at Rs. 120 is sold for Rs. 80. What is the rate of discount ?

(a) 25 ^{1}/_{5}%

(b) 26 ^{3}/_{5}%

(c) 29 ^{1}/_{7}%

(d) 33 ^{1}/_{3}%

**Answer:** (d) 33 ^{1}/_{3}%

M.P = Rs. 120

S.P = Rs. 80

Discount = M.P - S.P = 120 - 80 = Rs. 40

Discount % = ^{40}/_{120} X 100 = ^{100}/_{3} = 33 ^{1}/_{3}%

Q63. A chair listed at Rs. 1600 with a discount 20%. WHat additional discount must be offered to the customer to bring the net price Rs. 1000 ?

(a) 23%

(b) 25%

(c) 28%

(d) 31%

**Answer:** (c) 28%

List Price = Rs. 1600

Price after 20% discount = Rs. 1600 X 80% = Rs. 1600 X ^{80}/_{100} = Rs. 1280

Sale Price = Rs. 1000

∴ Additional discount = Rs. (1280 - 1000) = Rs. 280

Discount% = ^{280}/_{1000} X 100 = 28%

Q64. A man sold two cows for Rs. 20000 each. On one he gains 10% and other he losses 10%. Find his gain or loss percentage in the whole transaction.

(a) 0.99%

(b) 1.23%

(c) 1.5%

(d) 1.8%

**Answer:** (a) 0.99%

S.P of 1st cow = Rs. 20000

Gain = 10%

C.P of 1st Cow = | 100 | X 20000 |

100 + 10 |

= | 100 | X 20000 |

110 |

= Rs. 18,181.80

S.P of 2nd Cow = Rs 20000

Loss = 10%

C.P of 2nd Cow = | 100 | X 20000 |

100 - 10 |

= | 100 | X 20000 |

90 |

= Rs. 22,222.20

∴ C.P of two cows = Rs. (18181.80 + 22,222.20) = Rs. 40404

S.P of two cows = Rs. 40,000

∴ Loss = Rs. 404

Loss% = | 404 | X 100 |

40404 |

= 0.99%

Q65. By selling a goods for Rs. 1200, a shopkeeper loss 20%. At what price should he sell it to gain 5% ?

(a) Rs. 1350

(b) Rs. 1425

(c) Rs. 1465

(d) Rs. 1575

**Answer:** (d) Rs. 1575

S.P = Rs. 1200

Loss = 20%

∴ C.P = | 100 | X 1200 |

100 - 20 |

= | 100 | X 1200 |

80 |

= Rs. 1500

New S.P = | 100 + 5 | X 1500 |

100 |

= | 105 | X 1500 |

100 |

= Rs. 1575

Q66. A man sell an article at a profit of 10%. If he had bought it at 20% less and sold for Rs. 10 less, he would have gained 10%. Find the cost price of the article.

(a) Rs. 50

(b) Rs. 75

(c) Rs. 80

(d) Rs. 90

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

Let, the CP be Rs. x

∴ S.P = Rs | 110 | X x = Rs. | 11x |

100 | 10 |

New C.P = 80% of Rs. x = | 80x | = | 8x |

100 | 10 |

Gain = 25%

S.P = 125% of ^{8x}/_{10}

= | 125 | X | 8x | = Rs. x |

100 | 10 |

A/Q x - | 8x | = 10 |

10 |

⇒ | 2x | = 10 |

10 |

⇒ x = ^{100}/_{2} = Rs. 50

Q67. A grocer buys 30 kg of sugar at Rs. 20 per Kg and mixed it with 20 Kg of suger available at Rs. 35 per Kg. At what rate per kg should he sell mixture to gain 10% on the whole ?

(a) Rs. 28.60

(b) Rs. 31.25

(c) Rs. 32.85

(d) Rs. 36.50

**Answer:** (a) Rs. 28.60

CP of 50 Kg sugar = Rs. (30 X 20 + 20 X 35) = Rs. 600 + 700 = Rs. 1300

Gain = 10%

∴ S.P = Rs | 110 | X 1300 = Rs. 1430 |

100 |

∴ S.P per Kg = Rs | 1430 | = Rs. 28.60 |

50 |

Q68. On selling an article for Rs. 23, a man gains 15%. In order to gain 30% what will be the increase in its selling price ?

(a) Rs. 2

(b) Rs. 3

(c) Rs. 4

(d) Rs. 5

**Answer:** (b) Rs. 3

S.P = Rs. 23

Gain = 15%

∴ C.P = | 100 | X 23 |

100 + 15 |

= Rs. | 100 | X 23 = Rs. 20 |

115 |

New S.P = Rs. | 130 | X 20 = Rs. 26 |

100 |

Increase S.P = Rs. 26 - Rs. 23 = Rs. 3

Q69. A machine was sold at a gain of 10%. Had it been sold at Rs 700 less, the seller would have lost 10%. What is the cost price of the machine.

(a) Rs. 282

(b) Rs. 295

(c) Rs. 320

(d) Rs. 350

**Answer:** (d) Rs. 350

Let C.P be Rs x

∴ S.P = | 110 | X x = Rs | 11x |

100 | 10 |

New S.P = Rs. x X 90% = Rs. x X | 90 | = | 9x |

100 | 10 |

A/Q | 11x | - | 9x | = 70 |

10 | 10 |

⇒ 2x = 70 X 10 = 700

⇒ x = 350

Q70. A sweet seller mixes three varieties of sweets costing Rs. 50, Rs. 80 and Rs. 70 per Kg in the ratio 2 : 4 : 3 in terms of weight and sells the mixture at Rs. 60 per kg. What percentage of Loss does he make ?

(a) 13 ^{1}/_{3}%

(b) 13 ^{2}/_{5}%

(c) 14 ^{2}/_{7}%

(d) 15 ^{2}/_{9}%

**Answer:** (c) 14 ^{2}/_{7}%

Let the amount of varities of sweets in the mixture be 2x, 4x, 3x Kg

∴ C.P = Rs. [2x X 50 + 4x X 80 + 3x X 70] = Rs. [100x + 320x + 210x] = Rs 630x

S.P = Rs. 60 X 9x = Rs. 540x

Loss = Rs. 630x - 540x = Rs. 90x

Loss% = | 90x | X 100 = 14 | 2 | % |

630x | 7 |

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