Class 10MathematicsPair of Linear Equations in Two VariablesTextbook - Pair of Linear Equations in Two Variables
MediumForm the pair of linear equations in the following problems,and find their solutions (if they exist) by the 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?
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?
(N/A) Let the present age of Nuri be $x$ years and the present age of Sonu be $y$ years.
According to the given information:
Five years ago,Nuri's age was $(x-5)$ and Sonu's age was $(y-5)$.
$(x-5) = 3(y-5)$
$x - 5 = 3y - 15$
$x - 3y = -10$ $...(1)$
Ten years later,Nuri's age will be $(x+10)$ and Sonu's age will be $(y+10)$.
$(x+10) = 2(y+10)$
$x + 10 = 2y + 20$
$x - 2y = 10$ $...(2)$
Subtracting equation $(1)$ from equation $(2)$:
$(x - 2y) - (x - 3y) = 10 - (-10)$
$x - 2y - x + 3y = 10 + 10$
$y = 20$
Substituting $y = 20$ in equation $(1)$:
$x - 3(20) = -10$
$x - 60 = -10$
$x = 50$
Thus,the present age of Nuri is $50$ years and the present age of Sonu is $20$ years.
According to the given information:
Five years ago,Nuri's age was $(x-5)$ and Sonu's age was $(y-5)$.
$(x-5) = 3(y-5)$
$x - 5 = 3y - 15$
$x - 3y = -10$ $...(1)$
Ten years later,Nuri's age will be $(x+10)$ and Sonu's age will be $(y+10)$.
$(x+10) = 2(y+10)$
$x + 10 = 2y + 20$
$x - 2y = 10$ $...(2)$
Subtracting equation $(1)$ from equation $(2)$:
$(x - 2y) - (x - 3y) = 10 - (-10)$
$x - 2y - x + 3y = 10 + 10$
$y = 20$
Substituting $y = 20$ in equation $(1)$:
$x - 3(20) = -10$
$x - 60 = -10$
$x = 50$
Thus,the present age of Nuri is $50$ years and the present age of Sonu is $20$ years.
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