Question

A boy's age is. 1/4 that of his father. After 24 years the boy will be half the age of his father. Find their present ages.

Answer 1

Let. x = boy age and y = father age

x/4 = y
x = 4y ---(1)
(x+24)/2 =(y+24)
x+24 = 2y+48
x-2y = 24 ----(2)

on putting x= 4y from equation (1) we get
4y-2y = 24
2y =24
y = 12
on putting y= 12 on equation (1) we get
x=4(12)
x=48

Answer 2

Let the age  of  father  be 4x years

age  of  son = x years

After 20 years

Age  of  father = 4x + 24

Age  of  son = x +24

According to question, After 24 years the boy will be half the age of his father.

Age  of  son = 1/2× age  of father

$x+24=\frac{1}{2}(4x+24)\\\\2x+48=4x+24\\\\2x=24\\\\x=12$

Thus,

Age  of son = 12 years

Age of  father  = 4×12 = 48 years