# Ratio and Proportion

Q51. If the income of A is 10% more than that of B and the income of B is 10% less than that of C, then the incomes of A, B, C are in the ratio

(a) 79:80:100

(b) 89:80:100

(c) 89:90:100

(d) 99:90:100

**Answer:** (d) 99:90:100

Let, C's income be Rs. 100

∴ B's income = Rs. 90

∴ A's income = Rs. 110% of Rs. 90 = Rs. ^{110}/_{100} X 90 = Rs. 99

∴ A:B:C = 99:90:100

Q52. The average age of 3 girls is 20 years and their ages are in the proportion 3:5:7. The age of youngest girl is

(a) 12

(b) 13

(c) 14

(d) 15

**Answer:** (a) 12

Sum of their ages = 3 X 20 = 60

Let, the ages of the three girls be 3x, 5x, 7x

A/Q 3x + 5x + 7x = 60

⇒ 15x = 60

⇒ x = 4

∴ Age of the youngest girl = 3 X 4 = 12

Q53. The ratio of the number of students studying in school A, B, C is 5:6:8. If the number of students in each of the schools is decreased by 5%, 10% and 15% respectively. What will be the new ratio of the students in school A, B and C ?

(a) 88:108:112

(b) 92:108:126

(c) 95:108:136

(d) 98:108:148

**Answer:** (c) 95:108:136

Let the number of students in A, B, C be 5x, 6x and 8x respectively.

New strength = (95% of 5x), (90% of 6x), (85% of 8x)

= ^{95}/_{100} X 5x, ^{90}/_{100} X 6x, ^{85}/_{100} X 8x

∴ New ratio = | 475x | : | 540x | : | 680x |

100 | 100 | 100 |

= 475x : 540x : 680x

= 95 : 108 : 136

Q54. Two numbers are in the ratio 5:7. If each number is decreased by 5, the ratio becomes 3:5. The numbers are

(a) ^{13}/_{2}, ^{23}/_{2}

(b) ^{21}/_{2}, ^{33}/_{2}

(c) ^{25}/_{2}, ^{35}/_{2}

(d) ^{35}/_{2}, ^{41}/_{2}

**Answer:** (c) ^{25}/_{2}, ^{35}/_{2}

Let, the numbers be 5x, 7x

A/Q | 5x - 5 | = | 3 |

7x - 5 | 5 |

⇒ 25x - 25 = 21x - 15

⇒ 4x = 10

⇒ x = ^{5}/_{2}

∴ The numbers are 5 X | 5 | , 7 X | 5 |

2 | 2 |

= ^{25}/_{2}, ^{35}/_{2}

Q55. If ^{1}/_{5} : ^{1}/_{x} :: ^{1}/_{x} : ^{1}/_{1.25}, then ^{1}/_{x} = ?

(a) ^{1}/_{2.5}

(b) ^{1}/_{2.7}

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

(d) ^{1}/_{3.5}

**Answer:** (a) ^{1}/_{2.5}

1 | : | 1 | = | 1 | : | 1 |

5 | x | x | 1.25 |

⇒ | ^{1}/_{5} |
= | ^{1}/_{x} |

^{1}/_{x} |
^{1}/_{1.25} |

⇒ | x | = | 1.25 |

5 | x |

⇒ x^{2} = 1.25 X 5 = 6.25

⇒ x = 2.5

⇒ ^{1}/_{x} = ^{1}/_{2.5}

Q56. A square and a circle have the same area. The ratio of the side of the square and the radius of the circle is

(a) √π : 1

(b) π : 1

(c) 1 : π

(d) 1 : √π

**Answer:** (a) √π : 1

Let the side of the square be x and radius of the circle be y

Then x^{2} = πy^{2}

⇒ | x^{2} |
= π |

y^{2} |

⇒ | x | = √π |

y |

∴ x : y = √π : 1

Q57. If P is proportional to Q and P = 6. When Q = 3 then what is the value of P when Q = 12 ?

(a) 14

(b) 16

(c) 20

(d) 24

**Answer:** (d) 24

P ∝ Q

⇒ P = KQ

⇒ 6 = K . 3

⇒ K = 2

Now P = KQ

⇒ P = 2 X 12 = 24

Q58. The ratio between the ages of Sita and Gita is 5:6 and the sum of there ages is 33 years. The ratio of their ages after 5 years will be ?

(a) 17 : 21

(b) 18 : 21

(c) 20 : 23

(d) 23 : 27

**Answer:** (c) 20 : 23

Let the ages of Sita and Gita be 5x, 6x

A/Q 5x + 6x = 33

⇒ 11x = 33

⇒ x = 3

After 5 years Sita's age = 5 X 3 + 5 = 20 years

After 5 years Gita's age = 6 X 3 + 5 = 23 years

Required ratio = 20 : 23

Q59. Third proportional of 0.12 and 0.36 is

(a) 1.08

(b) 1.21

(c) 1.26

(d) 1.57

**Answer:** (a) 1.08

Let the third proportional be x

∴ 0.12 : 0.36 = 0.36 : x

⇒ | 0.12 | = | 0.36 |

0.36 | x |

⇒ 0.12x = 0.36 X 0.36

⇒ x = | 0.36 X 0.36 | = 3 X 0.36 = 1.08 |

0.12 |

Q60. Third proportional of 0.12 and 0.36 is

(a) 1.08

(b) 1.21

(c) 1.26

(d) 1.57

**Answer:** (a) 1.08

Let the third proportional be x

∴ 0.12 : 0.36 = 0.36 : x

⇒ | 0.12 | = | 0.36 |

0.36 | x |

⇒ 0.12x = 0.36 X 0.36

⇒ x = | 0.36 X 0.36 | = 3 X 0.36 = 1.08 |

0.12 |