Question

12 years ago ramains age was 6 years more than half of the age of his mother ,6 years from now ramans mother will be 1.5 times as old as raman what is ramans present age ?

Answer 1

Step-by-step explanation:

Assumption: Let the present age of Raman be x years and that of his mother be y years.

x - 12 = 1/2 (y - 12) + 6

Or, x - 12 = 1y/2 - {(1/2) × 12} + 6

Or, x - 12 = 1y/2 - 6 + 6

Or, x - 12 = 1y/2

Or, x - 1y/2 = 12 _____________ equation i

y + 6 = 1.5 ( x + 6)

Or, y + 6 = 1.5x + (1.5 × 6 )

Or, y + 6 = 1.5x + 9

Or, - 1.5x + y = 9 - 6

Or, - 1.5x + y = 3

Or, 1.5x - y = - 3______________ equation ii

By elimination method :-

By eliminating x,

1.5 × eq.i - 1 × eq.ii

1.5x - 0.75y = 18

- 1.5x + y. = 3( as all the signs change)

0.25y = 21

y = 21 ÷ 0.25

y = 84

Now, substituting y in equation i....

x - 1y/2 = 12

Or,. x - {(1/2) × 84} = 12

Or,. x - 42 = 12

Or,. x = 12 + 42

Or,. x = 54

Therefore, Raman's present age is 54 years and his mother's present age is 84 years.