Form the pair of linear equations for the following problems and find their solution by elimination method:

Aftab tells his daughter, "seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be." Find their present ages.

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 42years and age of his daughter is 12years.