4 years ago, the respective ratio between $${1 \over 2}$$ of A’s age at that time and four times of B’s age at that time was 5: 12. Eight years hence $${1 \over 2}$$ of A’s age at that time will be less than B’s age at that time by 2 years. What is B’s present age ?

Let B's present age = $$x$$ years

and A's present age = $$y$$ years

Acc. to ques, => $$\frac{\frac{1}{2} (y - 4)}{4 (x - 4)} = \frac{5}{12}$$

=> $$6 (y - 4) = 20 (x - 4)$$

=> $$6y - 24 = 20x - 80$$

=> $$10x - 3y = 28$$ ------------(i)

Also, $$(x + 8) - \frac{1}{2} (y + 8) = 2$$

=> $$2x + 16 - y - 8 = 4$$

=> $$2x - y = -4$$ -------------(ii)

Applying the operation, (i) - 3*(ii), we get :

=> $$(10x - 6x) + (-3y + 3y) = 28 + 12$$

=> $$x = \frac{40}{4} = 10$$ years