Question

a man is 4 times as old as his son . after 16 years he will be only twice as old as his son find their present ages with solution

Answer 1

Define x:

Let the son be x years old

The man is 4x years old

Find the age in 16 years time:

Son = x + 16

Man = 4x + 16

Solve x:

Man will be twice as old his son

4x + 16 = 2(x + 16)

4x + 16 = 2x + 32

4x - 2x = 32 - 16

2x = 16

x = 8

Find their age:

Son = x = 8 years old

Man = 4x = 4(8) = 32 years old

Answer: The son is 8 years old and the man is 32 years old.

Answer 2

Let the age of son = x

Man's age = 4x

16 years later -

Son's age = x + 16

Man's age = 4x + 16

According to the given question -

Man's age will be twice as his son -

4x + 16 = 2(x + 16)

4x + 16 = 2x + 32

4x - 2x = 32 - 16

2x = 16

x = 16/2

x = 8.

Finding present ages of son and man -

Age of son = x = 8 years.

Age of man = 4x = 4(8) = 32 years.

Hence :

Son is 8 years

Man is 32 years.