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
common ratio between Rahul’s age and Haroon’s age
be *x*.

Therefore,
age of Rahul and Haroon will be 5*x*
years and 7*x*
years respectively. After 4 years, the age of Rahul and Haroon will
be (5*x *+
4) years and (7*x *+
4) years respectively.

According to the given question, after 4 years, the sum of the ages of Rahul and Haroon is 56 years.

∴
(5*x *+
4 + 7*x *+
4) = 56

12*x
*+ 8 = 56

On transposing 8 to R.H.S, we obtain

12*x*
= 56 − 8

12*x*
= 48

On dividing both sides by 12, we obtain

*x*
= 4

Rahul’s
age = 5*x*
years = (5 × 4) years = 20 years

Haroon’s
age = 7*x*
years = (7 × 4) years = 28 years

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