Question

A father is four times as old as his son.
In four years time, he will be three times
as old as his son. What are their present
ages? Father 32 years​

Answer 1

Given:-

Age of father is 4 times his son

To find:-

The present age of father and his son

Assumption:-

Let the age of son be x

Age of father = 4x

Solution:-

After 4 years,

Age of son = x + 4

Age of father = 4x + 4

ATQ,

$\sf{4x+4 = 3(x+4)}$

= $\sf{4x+4 = 3x+12)}$

= $\sf{4x-3x = 12-4}$

= $\sf{x = 8}$

Therefore:-

Age of son = x = 8 years

Age of father = 4x = 4×8 = 32 years.

Verification:-

After 4 years age of father must be 3 times to age of his son:-

$\sf{4x+4 = 3(x+4)}$

= $\sf{4\times8 + 4 = 3(8+4)}$

= $\sf{32+4 = 3\times12}$

= $\sf{36 = 36}$. [Hence Verified ✓]

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Answer 2

4x+4 = 3(x+4)

= 4x-3x = 12-4

= x = 8

Age of son = 8 years

Age of father = 32 years