Question

A is now half as old his father .12year ago the father was 3times as old as A. find there ages

Answer 1

Let the age of father be x.
Then the age of A will be
$\frac{x}{2}$

Age of the father 12 years ago was
$(x - 12)$
Also, Age of A 12 years ago was
$( \frac{x}{2} ) - 12$

It is given that age of the father was 3 times as old as A, 12 years ago.

So, derive the formula as
Age of father (12 yrs ago) = 3 * Age of A (12 yrs ago).
$(x - 12) = 3 \times ( \frac{x}{2} - 12)$
Cross multiplying the term in the bracket in RHS
$(x - 12) = 3 \times \frac{((x - 24))}{2}$
multiply the term in the bracket with 3 in the RHS and take the denominator outside.
$(x - 12) = \frac{1}{2} (3x - 72)$

Multiply both sides with 2 to cancel the denominator 2 in the RHS.

$2(x - 12) = 3x - 72$
Expand the LHS
$2x-24 = 3x - 72$
$3x-2x = 72 - 24$
$x = 48$
Age of A, = x/2 = 24