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Question
The ages of P and Q are in the ratio 7 : 5. Ten years hence, the ratio of their ages will be 9 : 7. Find their ages.
Solution
Let the common multiple be x.
So, P's age be 7x years and Q's age be 5x years.
10 years hence, means after 10 years.
As per the given condition,
`(7x + 10)/(5x + 10) = (9)/(7)`
⇒ 7(7x + 10) = 9(5x + 10)
⇒ 49x + 70 = 45x + 90
⇒ 49x - 45x = 90 - 70
⇒ 4x = 20
⇒ x = 5
P's age = 7 years = 7(5) = 35years
Q's age = 5x = 5(5) = 25 years
Hence, P's age is 35 years and Q's age is 25 years.
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