Question

The present age of Sowmya is one fourth that of her mother Sobhadevi. 20
years later, the age of sowmya will be half the age of her mother. Find the
their present ages.​

Answer 1

✥ Required Solution:−

Let the present age of Sowmya be x and her mother's age be y.

then Sowmya present age = x = ¼ y

⇒ 4x = y (eq 1)

20 years later Sowmya age will be half the age of her mother

⇒ ( 20 + x) = ½ (20 + y)

⇒ 2(20 + x) = 20 +y

⇒ 40 + 2x = 20+ y

⇒ 20 + 2x = y (eq 2)

from eq 1 and eq 2

4x = 20 + 2x = y

⇒ 4x - 2x = 20

⇒ 2x = 20

⇒ x = 20/2

⇒ x = 10 years

Therefore, present age of Sowmya is 10 years

from eq 1 present age of her mother = 4x = 4 × 10 = 40 years

20 years later Sowmya age = 20 + x = 20 + 10 = 30 years

20 years later mother's age = 20 + y = 20 + 40 = 60 years