# Percentage

Q41. The price of an article has been reduced by 20%. In order to restore it to the original price, the new proce must be increased by

(a) 23%

(b) 25%

(c) 26%

(d) 27%

**Answer:** (b) 25%

Let the original price be Rs. 100

Rducing price = 100 - 20 = Rs. 80

For getting Rs. 100

Rs. 80 is increased by = Rs. 20

∴ Rs. 1 is increaded by = Rs | 20 |

80 |

∴ Rs. 100 is increaded by = Rs | 20 | X 100 = 25% |

80 |

Q42. What percent is 5% of 7% ?

(a) 51 ^{3}/_{7}%

(b) 63 ^{3}/_{7}%

(c) 71 ^{3}/_{7}%

(d) 79 ^{3}/_{7}%

**Answer:** (c) 71 ^{3}/_{7}%

Required percent = | ^{5}/_{100} |
X 100 % |

^{7}/_{100} |

= | 5 | X 100 % |

7 |

= 71 | 3 | % |

7 |

Q43. A student who secures 20% marks in a test fails by 30 marks. Another student who secures 32% marks get 42 marks more than those required to pass. Pass percentage of marks is

(a) 25%

(b) 28%

(c) 30%

(d) 35%

**Answer:** (a) 25%

Let, the total marks be x

A/Q 20% of x + 30 = 32% of x - 42

⇒ | 20 | X x + 30 = | 32 | X x - 42 |

100 | 100 |

⇒ | x | + 30 = | 8x | - 42 |

5 | 25 |

⇒ | 8x | - | x | = 30 + 42 |

25 | 5 |

⇒ | 8x - 5x | = 72 |

25 |

⇒ | 3x | = 72 |

25 |

⇒ x = 72 X | 25 | = 24 X 25 = 600 |

3 |

Pass marks = | 20 | X 600 + 30 = 120 + 30 = 150 |

100 |

Pass % = | 150 | X 100 = 25% |

600 |

Q44. a is 5 times as large as b. The percent that b is less than a is

(a) 80%

(b) 85%

(c) 90%

(d) 95%

**Answer:** (a) 80%

a = 5b

b less than a by 4b

Percentage of b less than a by | 4b | X 100% = 80% |

5b |

Q45. The length and breadth of a rectangle are increased by 5% and 10% respectively. The area of the new rectangle so formed exceeds the area of former by

(a) 14.2%

(b) 15.5%

(c) 16.3%

(d) 18.5%

**Answer:** (b) 15.5%

Let the length of the rectangle = l

The breadth of the rectangle = b

∴ Area = l X b = lb

After increasing

length of the rectangle = l + l X 5% = l + ^{5l}/_{100} = ^{105l}/_{100}

breadth of the rectangle = b + 10% X b = b + ^{10b}/_{100} = ^{110b}/_{100}

Area = | 105 l | X | 110b |

100 | 100 |

= | 21 l | X | 11b |

20 | 10 |

= | 231 lb |

200 |

Area Increase = | 231 lb | -lb |

200 |

= | 31 lb |

200 |

Increase % = | ^{31 lb}/_{200} |
X100 |

lb |

= | 31 | X100 |

200 |

= 15.5 %

Q46. 40% of ? = 120

(a) 250

(b) 280

(c) 285

(d) 300

**Answer:** (d) 300

40% of x = 120

⇒ ^{40}/_{100} X x = 120

⇒ x = 120 X ^{10}/_{4} = 300

Q47.The income of a broken remains uncharged through the rate of the commission is increased from 3% to 4%. The percentage of slump in bussinedd is

(a) 20%

(b) 25%

(c) 30%

(d) 35%

**Answer:** (b) 25%

Let the bussiness value change from x to y

Then 3% of x = 4% of y

⇒ | 3x | = | 4y |

100 | 100 |

⇒ 3x = 4y

⇒ y = ¾ x

Decress in business = (x - ¾ x) = ^{x}/_{4}

Percentage slump in bussiness = | ^{x}/_{4} |
X 100 % |

x |

= | x | X 100 % |

4x |

= 25%

Q48. 0.05 is how many percent of 40

(a) 0.135

(b) 0.130

(c) 0.125

(d) 0.120

**Answer:** (c) 0.125

A/Q 40 X x% =0.05

⇒ 40 X | x | = 0.05 |

100 |

⇒ x = | 0.05 X 10 |

4 |

= | .5 |

4 |

= 0.125

Q49. Ram's salary is 20% less than Hari, then how many percent Hari's salary more than that of Ram ?

(a) 18%

(b) 20%

(c) 23%

(d) 25%

**Answer:** (d) 25%

Hari's salary is more than that of Ram by { | R | X 100 } % |

100 - R |

= | 20 | X 100 % |

100 - 20 |

= | 20 | X 100 % |

80 |

= 25%

Q50. A man's wages were decreased by 50%. Again the reduced wages were increased by 50%. He has a loss of

(a) 20%

(b) 25%

(c) 28%

(d) 30%

**Answer:** (b) 25%

Let the initial wages = Rs. 100

∴ Decrease wages = Rs. 50

Finally wages = 150% of Rs. 50

= | 150 | X 50 = 75 |

100 |

∴ He has a loss of 25%