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?

Answer 1

Given:

Suresh is half his father's age

After 20 years, his father's age will be one and a half times i.e., $1\frac{1}{2}$ times = $\frac{3}{2}$ times Suresh's age

To find:

His father's age now

Solution:

Let's assume,

"S" → Suresh's present age

"F" → father's present age

We have Suresh's present age is $\frac{1}{2}$ of his father's present age, so the eq. will be,

S = $\frac{1}{2}$ × F

⇒ F = 2S ....... (i)

Age after 20 years,

Suresh → (S + 20) years

Father → (F + 20) years

Also, we have Father's age after 20 years will be $\frac{3}{2}$ times that of Suresh's age, so the eq. will be,

F + 20 = $\frac{3}{2}$ × (S + 20)

⇒ 2(F + 20) = 3(S + 20)

⇒ 2F + 40 = 3S + 60

substituting F = 2S from (i), we get

⇒2(2S) + 40 = 3S + 60

⇒ 4S - 3S = 60 - 40

⇒ S = 20 years ← Suresh's present age

On substituting S = 20 years in eq. (i), we get

∴ F = 2S = 2 × 20 = 40 years

Thus, his father's age now is 40 years.

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