Q. 7 A5.0( 3 Votes )

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.

Answer :

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.


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