Problems on Ages
Q1. The sum of the ages of A and B is 63 years. After 6
years, the age of B will be four times that of the A. What
is the age of B ?
(a) 46 Years
(b) 50 Years
(c) 53 Years
(d) 60 Years
Answer:(c) 53 Years
Let the Present Age of A is x years
So the Present Age of B = (63 - x) Years
After 6 Years,
(63 - x) + 6 = 4(x + 6)
69 - x = 4x + 24
5x = 45
x = 9
So the present age of B is = (63 - x)= 63 - 9= 53 Years
Q2. Rohit is twice as old as Rakesh was two years ago. If
the difference between their ages be 4 years, how old is
Rohit today ?
(a) 5 Years
(b) 8 Years
(c) 10 Years
(d) 12 Years
Answer:(d) 12 Years
Let the age of Rakesh two year ago is x years
So the Present Age of Rohit is 2x Years and Present age of Rakesh is (x + 2) Years
So,
2x - (x + 2) = 4
2x - x - 2 = 4
x = 6
So the present age of Rohit is = 2 X 6 = 12 Years
Q3. The sum of the ages of 4 children born at the
intervals of 3 years each is 42 years. What is the age of
the youngest child ?
(a) 4 Years
(b) 6 Years
(c) 9 Years
(d) 10 Years
Answer:(b) 6 Years
Let the age of the youngest child is x years. So the age of other childs will be (x + 3), (x + 6) and (x + 9)
x + (x + 3) + (x + 6) + (x + 9) = 42
4x = 42 - 18
x = 6
So the age of the youngest child is = 6 Years
Q4. A is two years older than B who is twice as old as C.
If the total of the ages of A, B and C be 27 years, then how
old is B ?
(a) 9 Years
(b) 10 Years
(c) 7 Years
(d) 8 Years
Answer:(b) 10 Years
Let the age of C be x years, then the age of B = 2x and age of A = 2x + 2
Then, x + 2x + 2x + 2 = 27
5x = 25
x = 5
So the age of the B is = 2x = 2 X 5 = 10 Years
Q5. The sum of the present ages of a father and his son
is 60 years. Six year ago, father's age was five times the
age of the son. After 6 years, son's age will be ?
(a) 12 Years
(b) 16 Years
(c) 20 Years
(d) 24 Years
Answer:(c) 20 Years
Let the present age of son is x, so the age of father will be (60 - x)
Then, six years ago
(60 - x) -6 = 5(x - 6)
6x = 84
x = 14
So the age of son after 6 years = (x + 6) = 14 + 6 = 20 Years
Q6. The difference between the ages of two persons is 15
years. Ten years ago, the elder one was twice as old as
the young one. The present age of the elader person is ?
(a) 35 Years
(b) 36 Years
(c) 30 Years
(d) 25 Years
Answer:(a) 35 Years
Let the Present Age of younger one is x years
So the Present Age of elder one is (x + 15) Years
Then, (x + 15) - 10 = 2(x - 10)
x = 25
So the present age of elder person is = (x + 10)= 25 + 10 = 35 Years
Q7. The age of the father is 30 years more than the son's age. Ten years hence, the father's age will become three times the son's age that time. What is the son's present age in years ?
(a) 3 Years
(b) 4 Years
(c) 5 Years
(d) 5 Years
Answer:(c) 5 Years
Let the son's present age be X years. Then the father's present age is (X + 30) years
Father's age after 10 years = (X + 40) years
Son's age after 10 years = (X + 10) years
(X + 40) = 3(X +10)
X + 40 = 3X + 30
2X = 10
X = 5
Q8. The ages of Sita and Gita are in the ratio 8:15. After 9 years, the ratio of their ages will be 11:18. What is the difference between their ages ?
(a) 18 years
(b) 21 Years
(c) 22 Years
(d) 25 Years
Answer: (b) 21 Years
Let, the ages of Sita and Gita are 8x and 15x
| A/Q | 8x + 9 | = | 11 |
| 15x + 9 | 18 |
⇒ 18 (8x + 9) = 11 (15x + 9)
⇒ 144x + 162 = 165x + 99
⇒ 21x = 63
⇒ x = 3
Difference between their ages = 15X3 - 8X3 = 45 - 24 = 21 years
Q9. The sum of the ages of a father and his son is 50 years now. Four years ago, their ages were in the ratio of 2 : 1. The ratio of the ages of father and son after 10 years will be
(a) 2 : 3
(b) 3 : 2
(c) 4 : 3
(d) 3 : 4
Answer: (b) 3 : 2
Let the age of father be x years
∴ the age of son is 50 - x
| x - 4 | = | 2 |
| 50 - x - 4 | 1 |
| ⇒ | x - 4 | = | 2 |
| 46 - x |
⇒ x - 4 = 92 - 2x ⇒ 3x = 96 ⇒ x = 32
After 10 years, Father's age = 32 + 10 = 42
Son's age = (50 - 32) + 10 = 28
∴ Ratio = 42 : 28 = 3 : 2
Q10. The ratio of present ages of two brothers is 1 : 2 and 5 years back the ratio was 1 : 3. What will be the ratio of their ages after 10 years ?
(a) 2 : 3
(b) 3 : 4
(c) 4 : 3
(d) 5 : 3
Answer: (a) 2 : 3
Let, the ages of two brothers are x and 2x
| A/Q | x - 5 | = | 1 |
| 2x - 5 | 3 |
⇒ 3x - 15 = 2x - 5 ⇒ x = 10
Ratio after 10 years
| x + 10 | = | 10 + 10 | = | 20 | = | 2 |
| 2x + 10 | 2 X 10 + 10 | 30 | 3 |
= 2 : 3
Practice Test Exam