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Sum

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

Concept: Solving Linear Inequations

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