Mathematics
Form the pair of linear equations in the following problem, 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?
Linear Equations
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Answer
Let present age of Nuri be x years and age of Sonu be y years.
Given,
Five years ago, Nuri was thrice as old as Sonu.
⇒ (x - 5) = 3(y - 5)
⇒ x - 5 = 3y - 15
⇒ x - 3y - 5 + 15 = 0
⇒ x - 3y + 10 = 0 ……..(1)
Given,
Ten years later, Nuri will be twice as old as Sonu.
⇒ (x + 10) = 2(y + 10)
⇒ x + 10 = 2y + 20
⇒ x - 2y + 10 - 20 = 0
⇒ x - 2y - 10 = 0 ……..(2)
Subtracting equation (1) from equation (2), we get :
⇒ x - 2y - 10 - (x - 3y + 10) = 0
⇒ x - 2y - 10 - x + 3y - 10 = 0
⇒ y - 20 = 0
⇒ y = 20.
Substituting value of y in equation (1), we get :
⇒ x - 3(20) + 10 = 0
⇒ x - 60 + 10 = 0
⇒ x - 50 = 0
⇒ x = 50.
Hence, pair of linear equations are x - 3y + 10 = 0, x - 2y - 10 = 0, where x and y are the ages (in years) of Nuri and Sonu respectively; Age of Nuri (x) = 50, Age of Sonu (y) = 20.
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