Question
Six years ago, the ratio of the ages of Amit and Sumit was
5:6 respectively. Ten years hence, their age ratio will be 7:8. What is the current age of Sumit?Solution
ATQ,
Let the ages of Amit and Sumit 6 years ago be '5x' and '6x' respectively.
So, age of Amit after 10 years = 5x + 6 + 10 = (5x + 16) years
And, age of Sumit after 10 years = 6x + 6 + 10 = (6x + 16) years
ATQ,
(5x + 16) / (6x + 16) = 7 / 8
⇒ 8(5x + 16) = 7(6x + 16)
⇒ 40x + 128 = 42x + 112
⇒ 16 = 2x
⇒ x = 8
So, present age of Sumit = 6 × 8 + 6 = 54 years
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