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Q.

Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. The present age of Nuri and Sonu is ____ and ____ respectively.


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Detailed Solution

Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. The present age of Nuri and Sonu is 50 and 20 respectively.
The general form of linear equations in two variables is: ax + by + c = 0
Assume the present age of Nuri to be ‘x’ and Sonu’s as ‘y’.
Then according to the question, five years ago,
⇒(x-5)=3×(y-5) ⟶equation 1
Ten years later,
⇒(x+10)=2×(y+10)⟶ equation 2
Simplifying the two equations we get,
⇒3y-x=10 ⇒x-2y=10
Since the coefficients of one of the variables (x) are equal and opposite, we can simply add the two equations.
⇒3y-2y=10+10 ⇒y=20 Substituting the value of y in one of the equations,
⇒x-2y=10 ⇒x=10+2y ⇒x=10+2×20 ⇒x=50 Therefore, the required integers are 50 and 20 respectively.
 
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