Q] When the son will be as old as his father today, the sum of their ages then will be

126. When the father was as old as his son is today, the sum of their ages then was 38.

Find their present ages.

​

Present Age

Father

y yrs

Future

As per the First condition,

PAST

Difference

+

= 126

∴

x + x – y + x = 126

∴

3x – y = 126

.....(i)

As per the Second condition,

30 -

+

= 38

∴

y + y – x + y = 38

∴

– x + 3y = 38

.....(ii)

(x – y)

x + (x – y)

(x – y)

x +

x yrs

x

Son

Son

x yrs

Future

Past

Present Age

50 yrs

50 +

(20)

Age Difference

(50 – 30)

30 yrs

30 –

(20)

Age

Difference

50 yrs

30 yrs

y

y –(x – y)

y –

(x – y)

y yrs

Sol.

Multiplying (ii) by 3,

– 3x + 9y = 114 .....(iii)

Adding (i) and (iii),

3x – y = 126

–3x + 9y = 114

8y

∴ y = 30

Substituting y = 30 in (i)

3x

– 30

=

∴

3x

=

∴

3x

= 156

∴

x

∴

x

= 52

The present age of father and son is 52 years and 30 years respectively.

∴

Sol.

3x – y = 126

.....(i)

– x + 3 = 38

.....(ii)

Q] When the son will be as old as his father today, the sum of their ages then will be

126. When the father was as old as his son is today, the sum of their ages then was 38.

Find their present ages.

​

126

126

+

30

= 240