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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?

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Detailed Solution

Let the current age of the father be

x

years.
Therefore, Suresh’s present age will be

(\frac{1}{2}

x)

years =

\frac{x}{2}

years.
After 20 years,
Father’s age will be =

(x + 20)

years.
Suresh’s age will be =

(\frac{x}{2} + 20)

years.
Now, according to the question,
Father’s age after 20 years =

(1 + \frac{1}{2})

x Suresh’s age after 20 years

\Rightarrow x + 20 = \frac{3}{2}

(\frac{x}{2} + 20)

\Rightarrow x + 20 = \frac{3 x}{4} + (\frac{3}{2}

20)

\Rightarrow x + 20 = \frac{3 x}{4} + 30

\Rightarrow x + 20 = \frac{(3 x + 120)}{4}

\Rightarrow 4

(x + 20) = 3 x + 120

\Rightarrow 4 x + 80 = 3 x + 120

\Rightarrow 4 x - 3 x = 120 - 80

\Rightarrow x = 40

Therefore, father’s current age =

x

years =

40

years.

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