# Ratio and Proportion

Q61. Fourth proportional to 0.2, 0.15 and 0.4 is

(a) 0.2

(b) 0.3

(c) 0.4

(d) 0.5

**Answer:** (b) 0.3

Let the fourth proportional be x

∴ 0.2 : 0.15 = 0.4 : x

⇒ | 0.2 | = | 0.4 |

0.15 | x |

⇒ x = | 0.4 X 0.15 | = 2 X 0.15 = 0.3 |

0.2 |

Q62. The prices of a scooter and a bike are in the ratio 6:7. If the bike price is 5000 more than the scooter, then the price of the bike be

(a) Rs. 28000

(b) Rs. 32000

(c) Rs. 35000

(d) Rs. 39000

**Answer:** (c) Rs. 35000

Let the price of the scooter and bike be 6x, 7x respectively

A/Q 6x = 7x - 5000

⇒ x = 5000

∴ Price of the bike = Rs. 7 X 5000 = Rs. 35000

Q63. Gold is 19 times as heavy as water and copper is 9 times as heavy as water. The ratio in which these two metals be mixed so that the mixture is 15 times as heavy as water, is

(a) 3 : 1

(b) 3 : 2

(c) 2 : 3

(d) 4 : 3

**Answer:** (b) 3 : 2

Let 1 gm of gold be mixed with x gm of copper to get (1+x) gm of the mixture. Then

1G = 19W, 1C = 9W

1 gm of Gold + x gm copper = (1+x) gm of mixture

19 W + 9W X x = (1+x) X 15W

⇒ 6Wx = 4W

⇒ x = ^{2}/_{3}

Required ratio = 1 : ^{2}/_{3} = 3 : 2

Q64. A, B and C invested Rs. 18000, Rs 30000 and Rs 24000 respectively in a bussiness. At the end of the year, they earn a profit of Rs. 4800. A's share of profit is

(a) Rs. 800

(b) Rs. 900

(c) Rs. 1000

(d) Rs. 1200

**Answer:** (d) Rs. 1200

A : B : C = 18000 : 30000 : 24000 = 3 : 5 : 4

∴ A's profit = | 3 | X 4800 |

3 + 5 + 4 |

= | 3 | X 4800 |

12 |

= Rs. 1200

Q65. A, B, C subscribe Rs. 50000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35000, A receives

(a) Rs. 12200

(b) Rs. 13700

(c) Rs. 14250

(d) Rs. 14700

**Answer:** (d) Rs. 14700

Let, C's share be Rs. x

∴ B's share = Rs. (x+5000)

A's share = Rs. 4000 + x + 5000 = Rs. 9000 + x

A/Q x + (x + 5000) + 9000 + x = 50000

⇒ 3x + 14000 = 50000

⇒ 3x = 36000

⇒ x = 12000

Now A:B:C = 21000 : 17000 : 12000 = 21 : 17 : 12

A's profit = Rs | 21 | X 35000 |

21 + 17 + 12 |

A's profit = Rs | 21 | X 35000 |

50 |

= Rs. 14700

Q66. A began a bussiness with Rs. 4500 and was joined after wards by B with Rs. 5400. If the profits at the end of the year were divided in the ratio 2:1, B joined the bussiness after

(a) 2 months

(b) 4 months

(c) 5 months

(d) 7 months

**Answer:** (d) 7 months

Let, B remained the business for x months

Now A:B = 4500 X 12 : 5400 X x = 54000 : 5400x = 10 : x

A/Q 10 : x = 2 : 1

⇒ | 10 | = | 2 |

x | 1 |

⇒ 2x = 10 ⇒ x = 5

∴ B remained the business for 5 months

∴ B join the bussiness after (12 - 5) = 7 months

Q67. Ram, Sham and Rahim starts a business. Ram invests 2 times as much as Sham and Sham invest ^{3}/_{4} th of Rahim invest. Then the ratio of their capitals be

(a) 5:3:6

(b) 6:3:4

(c) 6:4:7

(d) 7:3:5

**Answer:** (b) 6:3:4

Let Rahim invest be Rs. x

∴ Sham invest Rs. ^{3}/_{4} X x = Rs. ^{3x}/^{4}

Ram invest Rs. 2 X ^{3x}/_{4} = Rs. ^{3x}/^{2}

∴ Ram : Sham : Rahim = | 3x | : | 3x | : x |

2 | 4 |

= 6x : 3x : 4x = 6 : 3 : 4

Q68. A, B and C are three partners in a bussiness. If A's capital is half of B's capital and C's capital is twice the B's capital. The ratio of their capital is

(a) 1:2:3

(b) 1:2:4

(c) 1:3:4

(d) 1:3:5

**Answer:** (b) 1:2:4

Let, the capital of B's be Rs. x

∴ Capital of A's be Rs. ^{x}/_{2}

C's capital = Rs. 2x

∴ A : B : C = | x | : x : 2x = x : 2x : 4x = 1 : 2 : 4 |

2 |

Q69. A, B and C start a business, each investing Rs. 20,000. After 5 months A withdraw Rs. 5000, B Rs. 4000 and C invested Rs. 6000 more. At the end of the year, a total profit of Rs. 69900 was recovered. What is the share of B ?

(a) Rs. 19205

(b) Rs. 20950

(c) Rs. 21200

(d) Rs. 21700

**Answer:** (c) Rs. 21200

A : B : C = (20000 X 5 + 15000 X 7) : (20000 X 5 + 16000 X 7) : (20000 X 5 + 26000 X 7)

= 205000 : 212000 : 282000

= 205 : 212 : 282

∴ B's share = Rs. 69900 X | 212 | = 21200 |

699 |

Q70. A, B, C enter into partnership. A invested Rs. 2500 and B invested Rs. 2000. At the end of the year, they gained Rs. 1100, out of which B get Rs. 320. C's capital was

(a) 2375

(b) 2450

(c) 2475

(d) 2550

**Answer:** (a) 2375

let, the C's capital be Rs. x

∴ A : B : C = 2500: 2000 : x

B's profit = | 2000 | X 1100 |

2500 + 2000 + x |

∴ 320 = | 2000 X 1100 | X 1100 = | 2200000 |

4500 + x | 4500 + x |

⇒ 320 X 4500 + 320x = 2200000

⇒ 320x = 2200000 - 1440000

⇒ x = 2375