Problems on Ages

1. Ten years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages?
A. 45	B. 40
C. 35	D. 30

Answer : Option C

Explanation :

Let the present age of P and Q be 3x and 4x respectively.

Ten years ago, P was half of Q in age

=> (3x – 10) = ½ (4x – 10)

=> 6x – 20 = 4x – 10

=> 2x = 10

=> x = 5

total of their present ages = 3x + 4x = 7x = 7 × 5 = 35

2. Father is aged three times more than his son Sunil. After 8 years, he would be two and a half times of Sunil's age. After further 8 years, how many times would he be of Sunil's age?
A. 4 times	B. 4 times
C. 2 times	D. 3 times

Answer : Option C

Explanation :

Assume that Sunil's present age = x.

Then father's present age = 3x + x = 4x

After 8 years, fathers age = 2 ½ times of Sunils' age

=> (4x+8) = 2 ½ × (x+8)

=> 4x + 8 = (5/2) ×(x + 8)

=> 8x + 16 = 5x+ 40

=> 3x = 40-16 = 24

=> x = 24/3 = 8

After further 8 years,

Sunil's age = x + 8+ 8 = 8+8+8 = 24

Father's age = 4x + 8 + 8 = 4 × 8 + 8 + 8 = 48

Father's age/Sunil's age = 48/24 = 2

3. A man's age is 125% of what it was 10 years ago, but 83 1/3 % of what it will be after ten 10 years. What is his present age?
A. 70	B. 60
C. 50	D. 40

Answer : Option C

Explanation :

Let the age before 10 years = x

Then 125x/100 = x + 10

=>125x = 100x + 1000

=> x = 1000/25 = 40

Present age = x + 10 = 40 +10 = 50

4. A man is 24 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
A. 23 years	B. 22 years
C. 21 years	D. 20 years

Answer : Option B

Explanation :

Let the present age of the son = x years

Then present age the man = (x+24) years

Given that in 2 years, man's age will be twice the age of his son

=> (x+24) +2 = 2(x+2)

=> x = 22

5. Present ages of Kiran and Syam are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Syam's present age in years?
A. 28	B. 27
C. 26	D. 24

Answer : Option D

Explanation :

Ratio of the present age of Kiran and Syam = 5 : 4

=> Let the present age of Kiran = 5x

Present age of Syam = 4x

After 3 years, ratio of their ages = 11:9

=> (5x + 3) : (4x + 3) = 11 : 9

=> (5x+3) / (4x+3) = 11/9

=> 9(5x + 3) = 11(4x + 3)

=> 45x + 27 = 44x + 33

=> x = 33-27 =6

Syam's present age = 4x = 4×6 = 24