Question 70

Two years ago, the respective ratio between A’s age at that time and B’s age at that time was 5 : 9. A's age three years ago was 13 years less than B’s age six years ago. What is B’s present age?

Solution

Let present age of A and B be $$x$$ and $$y$$ years respectively.

=> $$\frac{x - 2}{y - 2} = \frac{5}{9}$$

=> $$9x - 18 = 5y - 10$$

=> $$9x - 5y = 8$$ --------------(i)

Also, => $$(x - 3) = (y - 6) - 13$$

=> $$x - y = -16$$ --------------(ii)

Multiplying eqn(ii) by 9 and subtracting it from (i), we get :

=> $$(9x - 9x) + (-5y + 9y) = 8 + 144$$

=> $$4y = 152$$

=> $$y = \frac{152}{4} = 38$$ years

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