Q. Ten years back, Rohan’s age was four times the age of his son. Ten years hence, Rohan’s age will become twice the age of his son. Find out the sum of the present ages of Rohan and his son (in years).

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Solution

The correct option is C 70
$L e t t h e a g e o f t h e s o n b e x y e a r s .$

$N o w, 10 y e a r s b a c k : (R - 10) = 4 (x - 10)$

$\to R - 4 x = - 30 \dots . E q n . (i)$

$A l s o, 10 y e a r s h e n c e : (R + 10) = 2 (x + 10)$

$\to R - 2 x = 10 \dots . . E q n . (i i)$

Subtracting eqn (i) from (ii), we get

$2 x = 40 \to x = 20. S u b s t i t u t i n g t h i s v a l u e i n e q n . (i i), w e g e t :$

$R - 2 (20) = 10 o r R = 10 + 40 = 50 y e a r s$

$N o w, R = x = 50 + 20 = 70 y e a r s .$

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