Q. 7 B5.0( 1 Vote )

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

Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

Answer :

Let the present age of Nuri = x yr

And the present age of Sonu = y yr


Five years ago,


Nuri’s age = (x – 5)yr


Sonu’s age = (y – 5)yr


According to the question,


(x – 5) = 3(y – 5)


x – 5 = 3y – 15


x – 3y = – 10 …(i)


After ten years,


Aftab’s age = (x + 10)yr


Daughter’s age = (y + 10)yr


According to the question,


(x + 10) = 2(y + 10)


x + 10 = 2y + 20


x – 2y = 10 …(ii)


Now, we can solve this by an elimination method


On subtracting Eq. (ii) from (i) we get


x – 2y – x + 3y = 10 – ( – 10)


– 2y + 3y = 10 + 10


y = 20


On putting y = 20 in Eq. (i) we get


x – 3(20) = – 10


x – 60 = – 10


x = 50


Hence, the age of Nuri is 50 years and age of Sonu is 20 years.


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