Ratio and Proportion
Q41. The surface areas of two spheres are in the ratio 1 : 9. The ratio of their volumes is
(a) 1 : 27
(b) 2 : 28
(c) 3 : 29
(d) 4 : 36
Answer: (a) 1 : 27
Let, the radii of the spheres be r and R
| Now | 4πr2 | = | 1 |
| 4πR2 | 9 |
| ⇒ | r2 | = | 1 |
| R2 | 32 |
| ⇒ | r | = | 1 |
| R | 3 |
| ⇒ ( | r | ) 3 = ( | 1 | ) 3 |
| R | 3 |
| ⇒ | r3 | = | 1 |
| R3 | 27 |
| ⇒ | 4/3 πr3 | = | 1 |
| 4/3 πR3 | 27 |
∴ Ratio of volumes = 1 : 27
Q42. What must be substrated from each one of 21, 38, 55, 106 so that the remainders are proportional
(a) 4
(b) 6
(c) 9
(d) 12
Answer: (a) 4
Let the required number be x
| A/Q | 21 - x | = | 55 - x |
| 38 - x | 106 - x |
⇒ (21 - x)(106 - x) = (55 - x)(38 - x)
⇒ 2226 - 127x + x2 = 2090 - 93x + x2
⇒ 34x = 136
⇒ x = 4
Q43. If a:b = 1:2, b:c = 3:4, c:d = 4:5 then a:b:c:d = ?
(a) 2:4:8:12
(b) 3:6:9:12
(c) 3:4:8:12
(d) 3:6:8:10
Answer: (d) 3:6:8:10
We have a:b = 1:2 ⇒ a/b = ½ ⇒ b = 2a
b:c = 3:4 ⇒ b/c = 3/4 ⇒ c = 4b/3
c:d = 4:5
⇒ c/d = 4/5
⇒ 5c = 4d
| ⇒ d = | 5c | = | 5 | . | 4b | = | 5b |
| 4 | 4 | 3 | 3 |
| Now a:b:c:d = | b | : b : | 4b | : | 5b |
| 2 | 3 | 3 |
| = | b | X 6 : 6b : | 4b | X 6 : | 5b | X 6 |
| 2 | 3 | 3 |
= 3b : 6b : 8b : 10b
= 3 : 6 : 8 : 10
Q44. In a ratio which is equal to 3:10, if the antecedent is 60, then the consequent is
(a) 156
(b) 170
(c) 185
(d) 200
Answer: (d) 200
Let, the consequent be x
A/Q 60:x = 3:10
| ⇒ | 60 | = | 3 |
| x | 10 |
⇒ 3x = 60 X 10
| ⇒ x = | 60 X 10 |
| 3 |
= 200
Q45. What should be added to each of the four numbers 5, 13, 17, 35 to make them proportional ?
(a) 17/5
(b) 23/5
(c) 24/5
(d) 29/5
Answer: (b) 23/5
Let, the the required number be x
| A/Q | 5 + x | = | 17 + x |
| 13 + x | 35 + x |
⇒ (5 + x) (35 + x) = (17 + x) (13 + x)
⇒ 175 + 5x + 35x + x2 = 221 + 17x + 13x + x2
⇒ 175 + 40x = 221 + 30x
⇒ 10x = 46
⇒ x = 46/10 = 23/5
Q46. What should be substracted to each of the four numbers 7, 10, 30, 50 to make them proportional ?
(a) 45/23
(b) 50/17
(c) 55/21
(d) 57/23
Answer: (b) 50/17
Let, the the required number be x
| A/Q | 7 - x | = | 30 - x |
| 10 - x | 50 - x |
⇒ (7 - x) (50 - x) = (30 - x) (10 - x)
⇒ 350 - 7x - 50x + x2 = 300 - 30x - 10x + x2
⇒ 350 - 57x = 300 - 40x
⇒ 350 - 300 = 57x - 40x
⇒ 50 = 17x
⇒ x = 50/17
Q47. The ratio of boys and girls in a school is 4:5. When 2 more boys join, their ratio becomes 6:7. How many girls in the school ?
(a) 29
(b) 31
(c) 35
(d) 42
Answer: (c) 35
Let the no of boys and no of girls in the school be 4x and 5x respectively
| A/Q | 4x + 2 | = | 6 |
| 5x | 7 |
⇒ 28x + 14 = 30x
⇒ 30x - 28x = 14
⇒ 2x = 14
⇒ x = 7
∴ No of girls = 5 X 7 = 35
Q48. Find the mean proportional between 25 and 100
(a) 45
(b) 50
(c) 60
(d) 75
Answer: (b) 50
Mean Proportional =√(25 X 100) = 5 X 10 = 50
Q49. A boy contains one rupee, 50p and 25p coins in the ratio 8:9:11. If the total money in the bag is Rs. 244, find the number of coins of each type.
(a) 128, 144, 176
(b) 132, 153, 186
(c) 135, 156, 192
(d) 152, 163, 198
Answer: (a) 128, 144, 176
Let, the number of one-rupee, 50-p and 25-p coins be 8x, 9x, 11x respectively
Now 8x + 9x/2 + 11x/4 = 244
⇒ 32x + 18x + 11x = 976
⇒ 62x = 976
⇒ x = 16
No of one rupee coins = 8 X 16 = 128
No of 50-p coins = 9 X 16 = 144
No of 25-p coins = 11 X 16 = 176
Q50. 43.5:25 = ?
(a) 3
(b) 4
(c) 5
(d) 7
Answer: (b) 4
| 43.5:25 = | 43.5 |
| 25 |
| = | (22)3.5 |
| 25 |
| = | 27 |
| 25 |
= 22 = 4
Practice Test Exam