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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?
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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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