Question

The present age of Nancy is one - fourth that of her mother. 20 years later the age of Nancy will be half the age of her mother. Find their present ages and also ages after 20 years

Answer 1

Let the present age of Nancy be x and her mother's age be y.
then Nancy's present age = x = $\frac{1}{4}$y
⇒ 4x = y       (eq 1)
20 years later Nancy's age will be half the age of her mother
⇒ ( 20 + x) = $\frac{1}{2}$(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 Nancy is 10 years 
from eq 1 present age of her mother = 4x = 4*10 = 40 years
20 years later Nancy's age = 20 + x = 20 +10 = 30 years 
20 years later mother's age = 20 + y = 20 + 40 = 60 years