Aman’s age is three times his son’s age. Ten years ago he was five times his son’s age. Find their present ages.

Let Aman’s
son’s age be *x* years. Therefore, Aman’s age will
be 3*x* years. Ten years ago, their age was (*x* −
10) years and (3*x* − 10) years respectively.

According to the question,

10 years ago, Aman’s age = 5 × Aman’s son’s age 10 years ago

3*x*
− 10 = 5(*x* − 10)

3*x*
− 10 = 5*x* − 50

Transposing
3*x* to R.H.S and 50 to L.H.S, we obtain

50 −
10 = 5*x* − 3*x*

40 = 2*x*

Dividing both sides by 2, we obtain

20 = *x*

Aman’s
son’s age = *x* years = 20 years

Aman’s
age = 3*x* years = (3 × 20) years = 60 years

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