9.The ages of Rahul and Haroon are in the ratio 5 : 7. Four years later the sum of their ages will be 56 years. What are their present ages

Let the present ages of Rahul and Haroon he 5x years and 7x years respectively.
As per the conditions given we have

4 years later, the age of Rahul will be (5x + 4) years.

4 years later, the age of Haroon will be (7x + 4) years.

As per the conditions, we get

(5x + 4) + (7x + 4) = 56

\(\Rightarrow\) 5x + 4 + 7x + 4 = 56

\(\Rightarrow\) 12x + 8 = 56

\(\Rightarrow\) 12x = 56 – 8 (transposing 8 to RHS)

\(\Rightarrow\) 12x = 48

\(\Rightarrow\) x = 48 ÷ 12 = 4 (transposing 12 to RHS)

Hence, the required age of Rahul = 5 × 4 = 20 years.

and the required age of Haroon = 7 × 4 = 28 years.