Question 49

Two years ago, A’s age was $${1 \over 2}$$ of B’s age at that time. A’s age four years hence will be 22 years less than B’s age eight years hence. What is B’s present age ?

Solution

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

Acc. to ques, => $$(x - 2) = \frac{1}{2} (y - 2)$$

=> $$2x - 4 = y - 2$$

=> $$2x - y = 2$$ -------------(i)

Also, $$(x + 4) = (y + 8) - 22$$

=> $$x - y = -18$$ ------------(ii)

Multiplying eqn(ii) by 2 and subtracting it from (i), we get :

=> $$(2x - 2x) + (-y + 2y) = (2 + 36)$$

=> $$y = 38$$ years

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