# Problems on Profit Loss

Q51. A shopkeeper sold a TV set for Rs. 17940 with a discount of 8% and earned a profit of 19.6%. Wht would have been the percentage of profit earned if no discount was offered.

(a) 23.07%

(b) 23.89%

(c) 24.56%

(d) 24.98%

**Answer:** (a) 23.07%

S.P = 92% of Rs. 17940

= Rs. 92/100 X 17940 = Rs. 16504.80

Profit = 19.6 %

At selling price Rs. 119.6 cost price be Rs. 100

∴ At selling price Rs. 1 cost price be Rs. 100/119.6

∴ At selling price Rs. 16504.80 cost price be Rs. (100/119.6) X 16504.80 = Rs. 13800

∴ C.P = Rs. 13800

S.P = Rs. 17940

∴ Profit = Rs. (17940 - 13800) = Rs. 4140

Profit % = (4140/17940) X 100 = 23.07 %

Q52. The marked price of a shirt and trousers are in the ratio 1:2. The shopkeeper gives 40% discount on the shirt. If the total discount on both is 30%, the discount offered on the trouser is

(a) 21%

(b) 23%

(c) 25%

(d) 29%

**Answer:** (c) 25%

Let, the marked price of shirt be Rs. x

and the marked price of trousers be Rs. 2x

Let, the discount of trousers be y%

A/Q x X 40% + 2x X y% = (x + 2x) X 30%

⇒ | 40x | + | 2xy | = | 30 X 3x |

100 | 100 | 100 |

⇒ 40x + 2xy = 90x

⇒ 50x = 2xy

⇒ y = 50x/2x = 25

So answer is 25%

Q53. A wholeseller sells 20 pens at the marked price of 16 pens to a retailer. The retailer in turn sells them at the marked price. The gain percent to the retailer is

(a) 18%

(b) 22%

(c) 24%

(d) 25%

**Answer:** (d) 25%

Let, the M.P of each pen be Rs. x

∴ S.P of 20 pens = M.P of 16 pens = Rs. 16 X x = Rs. 16x

∴ Retailer C.P of 20 pens = Rs. 16x

Retailer S.P of 20 pens = Rs. 20 X x = Rs. 20x

∴ Gain = Rs. (20x - 16x) = Rs. 4x

∴ Gain % = 4x/16x X 100 = 25%

Q54. A shopkeeper claims to sell his articles at a discount of 10%, but marks his articles by increasing the cost of each by 20%. His gain percent is

(a) 8%

(b) 12%

(c) 14%

(d) 17%

**Answer:** (a) 8%

Let the C.P be Rs. 100

∴ M.P = Rs. 120

∴ S.P = Rs. (90/100) X 120 = Rs. 108

Gain = Rs. (108 - 100) = Rs. 8

Gain % = (8/100) X 100 = 8%

Q55. If the manufacturer gains 10%, the wholesale dealer 15% and the retailer 25%, then the cost of production of an article whose retail price is Rs. 1265 is

(a) Rs. 800

(b) Rs. 850

(c) Rs. 925

(d) Rs. 975

**Answer:** (a) Rs. 800

Let, the cost of production be Rs. x

Now x X | 110 | X | 115 | X | 125 | = 1265 |

100 | 100 | 100 |

⇒ x X | 11 | X | 23 | X | 25 | = 1265 |

10 | 20 | 20 |

⇒ x = | 1265 X 10 X 20 X 20 |

11 X 23 X 25 |

= 800

∴ Answer is Rs. 800

Q56. A fruit seller buys lemons at 2 for a rupee and sells them at 5 for 3 rupees. His gain percent is

(a) 17%

(b) 20%

(c) 22%

(d) 26%

**Answer:** (b) 20%

C.P of 2 lemon = Rs. 1

C.P of 1 lemon = Rs. ½

S.P of 5 lemon = Rs. 3

S.P of 1 lemon = Rs. 3/5

Gain = Rs. ( | 3 | - | 1 | ) = Rs. | 6 - 5 | = Rs. | 1 |

5 | 2 | 10 | 10 |

Gain % = | 1/10 | X 100 = | 2 | X 100 = 20% |

½ | 10 |

Q57. A shopkeeper sells a badminton racket whose marked price is Rs. 30 at a discount of 25% and gives a shuttlecock costing Rs. 1.50 free with each racket. Even then he makes a profit of 20%. His cost price per racket is

(a) Rs. 17

(b) Rs. 20

(c) Rs. 22

(d) Rs. 24

**Answer:** (b) Rs. 20

M.P = Rs. 30

Discount = 15% and Rs. 1.50

∴ S.P = Rs. ( | 85 | X 30 - 1.50 ) |

100 |

= Rs. ( | 51 | - | 3 | ) |

2 | 2 |

= Rs. 48/2 = Rs. 24

∴ Gain % = 20%

∴ C.P = Rs. ( | 100 | X 24 ) = Rs.20 |

120 |

Q58. An article passing through two hands, is sold at a profit of 38% at the original cost price. If the first dealer makes a profit of 20%, then the profit percent made by the second is

(a) 8%

(b) 12%

(c) 15%

(d) 18%

**Answer:** (c) 15%

Let, the C.P be Rs. 100

∴ S.P = Rs. 138

Let, the profit made by 2nd dealer be x%

∴ (100 + x)% of 120% of Rs. 100 = Rs. 138

⇒ | 100 + x | X | 120 | X 100 = 138 |

100 | 100 |

⇒ 12000 + 120x = 13800

⇒ 120x = 13800 - 12000 = 1800

⇒ x = 1800/120 = 15

Q59. A merchant purchases a wrist watch for Rs. 450 and fixed the list price in such a way that after allowing a discount of 10% he earns a profit of 20%. The list price of the watch is

(a) Rs. 475

(b) Rs. 490

(c) Rs. 550

(d) Rs. 600

**Answer:** (d) Rs. 600

C.P = Rs. 450

Gain = 20%

∴ S.P = Rs. (120/100) X 450 = Rs. 540

Let the list price be Rs. x

∴ 90% of x = 540

⇒ (90/100) X x = 540

⇒ x = (540 X 100)/90 = 600

∴ Answer is Rs. 600

Q60. Two thirds of a consignment was sold at a profit of 6% and the rest at a loss of 3%. If there was an overall profit of Rs. 540, the value of consignment was

(a) Rs. 14750

(b) Rs. 15000

(c) Rs. 16500

(d) Rs. 18000

**Answer:** (d) Rs. 18000

Let, the value of consignment be Rs. x

∴ S.P = Rs. ( | 2 | X x X | 106 | X | 1 | X x X | 97 | ) |

3 | 100 | 3 | 100 |

= Rs. ( | 53x | + | 97x | ) |

75 | 300 |

= Rs. | 212x + 97x |

300 |

= Rs. | 309 | x |

300 |

∴ | 309 | - x = 540 |

300 |

⇒ 9x/300 = 540

⇒ x = (540 X 300)/9 = 18000

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