Question

a father is 4 times as old as his son now.After 24 years he would be twice as old as his son . What are he present ages of the father and the son ?

Answer 1

Answer:

Let son's age is x years

father is 4 times older than his son hence father age will be 4x

In 20 years he will be twice as old as his son. After 20 years their ages will be

Son age = x + 20

Father's age = 4x + 20

4x + 20 = 2 ( x + 20 )

Solving the equation

4x + 20 = 2x + 40

4x - 2x = 40 - 20

2x = 20

x = 10

The son's present age is 10 years

Father's age is 4x= 4 × 10 = 40 years.

Answer son's present age 10 years and father's present age is 40 years

Let us check the correctness of answer by putting their respective ages in the equation.

4x + 20 = 2x + 40

4 × 10 + 20 = 2×10 + 40

40 + 20 = 20 + 40

60 = 60

Means answer is correct.

Let the present age of the sun be ‘x’ and that of the father be ‘y’

Then as per the question

4x = y ——-(i)

and 2(x+20) = y+20 ——-(ii)

Substituting the value of y from (i) in (ii), we get

2(x+20) = 4x +20

or 2x+40 = 4x+20

or 4x-2x = 40–20

or 2x = 20

or x=10

Substituting the value of ‘x’ thus obtained in (i), we get

y = 4x = 4*10 = 40

Therefore the present age of father is 40 years and that of the son is 10 years