Question

Question 2 (ii)
Form 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?

Answer 1

Let the present age of Nuri = x
And, the present age of Sonu = y
According to the given information,
(x - 5) = 3(y - 5)
$\Rightarrow$ x - 3y = -10 ... (i)
$\Rightarrow$ (x + 10) = 2(y + 10)
$\Rightarrow$ x - 2y = 10 ... (ii)
Subtracting equation (i) from equation (ii), we get
y = 20 ... (iii)
Putting this value in equation (i), we get
x - 60 = -10
$\Rightarrow$ x = 50
Hence, age of Nuri = 50 years and age of Sonu = 20 years.