Question

A person's present age is two-fifth of the age of his mother. after 8 years, he will be one-half of the age of his mother. how old is the mother at present? answers

Answer 1

let x be current age of mother
y be current age of person
x2/5=y-----------------eqn 1

y+8=3x/2---------eqn2

from 1

x=5y/2
putting it in 2
y+8=15y/4
4y+32=15y
11y=32
y=32/11 years
age of mother
x=5*32/22

Answer 2

Answer :-

⇒ 40 years

Explanation :-

• Let present age of mother = 'x' years

• Person's age = 2/5 x

After Eight Years :-

• Son's age = 2/5 x + 8

• Mother's age = x + 8

According to the Question :-

⇒ 2x/5 + 8 = 1/2 (x + 8)

⇒ 40 + 2x/5 = x/2 + 4

⇒ 40 + 2x = 5/2x + 20

⇒ 40 - 20 = ( 5/2 - 2) x

⇒ 20 = x/2

⇒ x = 40 years

Present Age of Mother :-

• x = 40 years

Present age of Son :-

• 2/5 (40) + 8 = 24 years

Verification :-

⇒ 2(40)/5 + 8 = 1/2 (40 + 8)

⇒ 16 + 8 = 1/2 (48)

⇒ 24 = 24

L.H.S = R.H.S

Hence verified