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 |
⇒ x2 = 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 x2 = πy2
⇒ | x2 | = π |
y2 |
⇒ | 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 |
Practice Test Exam