10. 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 the present age of the son be x years.
Present age of Aman = 3x years

Also,10 years ago, the son’s age was = (x – 10) years

10 years ago, the father’s age was = (3x – 10) years

As per the conditions, we have

5(x – 10) = 3x – 10

\(\Rightarrow\)5x – 50 = 3x – 10

\(\Rightarrow\) 5x – 3x = 50 – 10[Transposing 3x to LHS and 50 to RHS]

\(\Rightarrow\) 2x = 40

\(\Rightarrow\)x = 40 ÷ 2 = 20

Hence,we have,

The son’s age = 20 years.

and the age of Aman = 20 × 3 = 60 years.