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?
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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