Question 69

Three years ago, the respective ratio between A’s age at that time and B’s age at that time was 9 : 5. If A’s age two years hence will be 17 years more than B’s age five years hence, what is B’s present age?

Solution

Let present ages of A and B = $$x$$ years and $$y$$ years respectively.

=> $$\frac{x - 3}{y - 3} = \frac{9}{5}$$

=> $$5x - 15 = 9y - 27$$

=> $$5x - 9y = -12$$ --------------(i)

Also, $$(x + 2) = 17 + (y + 5)$$

=> $$x - y = 20$$ --------------(ii)

Multiplying eqn(ii) by 5 and then subtracting (i) from it, we get :

=> $$(5x - 5x) + (9y - 5y) = 100 + 12$$

=> $$y = \frac{112}{4} = 28$$ years

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