# Percentage

Q31. If the price of sugar falls by 5%, by how much percent must a house holder increase its consumption, so as not to decrease its expenditure on sugar ?

(a) 3 ^{3}/_{19} %

(b) 5 ^{5}/_{19} %

(c) 7 ^{7}/_{19} %

(d) 9 ^{9}/_{19} %

**Answer:** (b) 5 ^{5}/_{19} %

Increase % in consumption = { | R | X 100 } % |

100 - R |

= | 5 | X 100 % |

100 - 5 |

= | 5 | X 100 % |

95 |

= | 100 | % |

19 |

= 5 | 5 | % |

19 |

Q32. If 10% of A = 20% of B = ^{1}/_{5} of C, then A:B:C is

(a) 2:1:1

(b) 1:2:1

(c) 1:1:2

(d) 1:2:2

**Answer:** (a) 2:1:1

10% of A = 20% of B = ^{1}/_{5} of C

⇒ | 10 | X A = | 20 | X B = | 1 | X C |

100 | 100 | 5 |

⇒ | A | = | B | = | C |

10 | 5 | 5 |

⇒ | A | = | B | = | C |

2 | 1 | 1 |

∴ A:B:C = 2 : 1 : 1

Q33. 4 liters of water is added to 20 liters of a mixture of a 40% solution of alcohol in water. The strength of alcohol is now ?

(a) 23 ^{1}/_{3} %

(b) 27 ^{1}/_{3} %

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

(d) 37 ^{1}/_{3} %

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

Alcohol in 20 liters of mixture = | 40 | X 20 liters = 8 liters |

100 |

Now, alcohol in 24 liters of mix = 8 liters

∴ Strength of alcohol = | 8 | X 100 % |

24 |

= 33 | 1 | % |

3 |

Q34. By how much is 30% of 80 greater than ^{5}_{6} of 24 ?

(a) 3

(b) 4

(c) 5

(d) 7

**Answer:** (b) 4

30% of 80 = | 30 | X 80 = 24 |

100 |

5 | of 24 = | 5 | X 24 = 20 |

6 | 6 |

Required no = 24 - 20 = 4

Q35. x % of y is y % of ?

(a) x

(b) xy

(c) xy^{2}

(d) x^{2}

**Answer:** (a) x

x % of y = | x | X y = | xy |

100 | 100 |

Now y% of ? = | xy |

100 |

⇒ | y | X ? = | xy |

100 | 100 |

⇒ ? = | xy | X | 100 | = x |

100 | y |

Q36. When a number is first increased by 10% and then reduced by 10% the number

(a) 1%

(b) 2%

(c) 5%

(d) 10%

**Answer:** (a) 1%

Let the number be x

After increasing, the new number be = x + x X 10%

= x + | 10x |

100 |

= | 11x |

10 |

Reducing by the new number by 10% = | 11x | - | 11x | X 10 % |

10 | 10 |

= | 11x | - | 11x | X | 10 |

10 | 10 | 100 |

= | 11x | - | 11x |

10 | 100 |

= | 110x - 11x |

100 |

= | 99x |

100 |

Decrease = (x - | 99x | ) = | x |

100 | 100 |

Decrease %= | ^{x}/_{100} |
X 100% |

x |

= | x | X 100% = 1 % |

100x |

Q37. What is 30% of 30% equal to ?

(a) 0.06

(b) 0.09

(c) 0.12

(d) 0.15

**Answer:** (b) 0.09

Let the number be x

∴ x = 30% of 30%

= | 30 | X | 30 |

100 | 100 |

= | 9 |

100 |

= 0.09

Q38. If the side of a square is decreased by 10% then its area is decreased by ?

(a) 10%

(b) 12%

(c) 16%

(d) 19%

**Answer:** (d) 19%

Let the side of a square be x

∴ Area of the square = x X x = x^{2}

After decreasing

side of the square be = x - x X 10 % = x - ^{10x}/_{100} = ^{9x}/_{10}

∴ Area of the new square = | 9x | X | 9x | = | 81x^{2} |

10 | 10 | 100 |

∴ Decrease in Area = x^{2} - |
81x^{2} |
= | 19x^{2} |

100 | 100 |

∴ Decrease % = | ^{19x2}/_{100} |
X 100 % |

x^{2} |

= | 19x^{2} |
X 100 % |

100x^{2} |

= 19 %

Q39. Which number is 40% less than 70 ?

(a) 49

(b) 46

(c) 45

(d) 42

**Answer:** (d) 42

Let the required number be x

A/Q x = 70 - 70 X 40 %

= 70 - 70 X | 40 |

100 |

= 70 - 28 = 42

Q40. The price of an article has been reduced by 20%. In order to restore

(a) 49

(b) 46

(c) 45

(d) 42

**Answer:** (d) 42

Let the required number be x

A/Q x = 70 - 70 X 40 %

= 70 - 70 X | 40 |

100 |

= 70 - 28 = 42