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Question
The ages of A and B are in the ratio 7 : 5. Ten years hence, the ratio of their ages will be 9 : 7. Find their present ages.
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Solution
Ratio in the present ages of A and B = 7 : 5
Let age of A = 7x years
Let age of B = 5x years
10 years hence,
Then age of A = 7x + 10 years
and age of B = 5x + 10 years
According to the condition,
By crossing multiplication
7(7x + 10) = 9(5x + 10)
⇒ 49x + 70 = 45x + 90
⇒ 49x – 45x = 90 – 70
⇒ 4x = 20
⇒ x = 5
Present age of A = 7x = 7 x 5 = 35 years
and present age of B = 5x = 5 x 5 = 25 years
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