Let the present age of father i.e. Aftab = x yr
And the present age of his daughter = y yr
Seven years ago,
Aftab’s age = (x – 7)yr
Daughter’s age = (y – 7)yr
According to the question,
(x – 7) = 7(y – 7)
⇒ x – 7 = 7y – 49
⇒ x – 7y = – 42 …(i)
After three years,
Aftab’s age = (x + 3)yr
Daughter’s age = (y + 3)yr
According to the question,
(x + 3) = 3(y + 3)
⇒ x + 3 = 3y + 9
⇒ x – 3y = 6 …(ii)
Now, we can solve this by an elimination method
On subtracting Eq. (ii) from (i) we get
x – 3y – x + 7y = 6 – ( – 42)
⇒ – 3y + 7y = 6 + 42
⇒ 4y = 48
⇒ y = 12
On putting y = 12 in Eq. (ii) we get
x – 3(12) = 6
⇒ x – 36 = 6
⇒ x = 42
Hence, the age of Aftab is 42 years and age of his daughter is 12 years.