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Question
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?
Solution
Let common ratio between Rahul’s age and Haroon’s age be x.
Therefore, age of Rahul and Haroon will be 5x years and 7x years respectively. After 4 years, the age of Rahul and Haroon will be (5x + 4) years and (7x + 4) years respectively.
According to the given question, after 4 years, the sum of the ages of Rahul and Haroon is 56 years.
∴ (5x + 4 + 7x + 4) = 56
12x + 8 = 56
On transposing 8 to R.H.S, we obtain
12x = 56 − 8
12x = 48
On dividing both sides by 12, we obtain
`(12x)/12 = 48/12`
x = 4
Rahul’s age = 5x years = (5 × 4) years = 20 years.
Haroon’s age = 7x years = (7 × 4) years = 28 years.
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