Question

Suresh is half his father’s age. After 20 years, his father’s age will be one and a half times Suresh's age. What is his father’s age now?
[a] 40
[b] 20
[c] 26
[d] 30

Answer 1

Hint: Assume that the present age of Suresh is x and hence the present age of his father 2x. Use the fact that after 20 years, the age of Suresh is x+20 and the age of his father, 2x+20. Hence form an equation in x. Solve the equation for x and hence find the present age of Suresh and his father. Verify your answer.

Complete step-by-step answer:
Let the present age of Suresh be x.
Since the present age of Suresh’s father is twice the age of Suresh, we have the present age of Suresh’s father = 2x.
Now after twenty years, the age of Suresh = x+20 and the age of Suresh’s father = 2x+20.
Since after twenty years, Suresh’s father's age is one and half of the age of Suresh, we have
$2x+20=1\dfrac{1}{2}\left( x+20 \right)\Rightarrow 2x+20=\dfrac{3}{2}\left( x+20 \right)$
Multiplying both sides by 2, we get
$4x+40=3x+60$
Subtracting 40 from both sides, we get
$4x=3x+20$
Subtracting 3x from both sides, we get
$x=20$
Hence, the present age of Suresh is 20 and hence the present age of Suresh’s father $=2\times 20=40$
Hence option [a] is correct.

Note: Verification:
The present age of Suresh = 20
The present age of Suresh’ father = 40
Ratio $=\dfrac{20}{40}=\dfrac{1}{2}$
Hence, the present age of Suresh is half his father.
Age of Suresh’s father after 20 years = 60
Age of Suresh after 20 years = 40
Ratio $=\dfrac{60}{40}=\dfrac{3}{2}=1\dfrac{1}{2}$
Hence after twenty years, Suresh’s father’s age is one and half of his age.
Hence our answer is verified to be correct.