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
Practice Test Exam