The sum of the ages of a daughter and mother is 56 years; after four years the age of the mother will be three times that of the daughter. What is the age of the daughter and the mother respectively?

Let the present age of the mother be x years and the present age of the daughter be y years
According to the question, x + y = 56 ...... (i)
After 4 years, age of the Mother = x + 4
Age of the daughter after 4 years = y + 4
So,
x + 4 = 3 (y + 4) ...... (ii)
x + 4 = 3y + 12
From the equation (i) we get, x = 56 - y
Thus, keep the value of x in equation 2, we get
(56 - y) + 4 = 3y + 12
⇒60 – y = 3y + 12
⇒y = 12
So, the daughter’s present age is 12 years
Mother’s present age = 56-12 = 44 years