Question

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

Hint: In the question, we are given a word problem and we have to solve it by taking variables and solving equations. We will assume the present age of Nuri and Sonu as x and y. And using information in the question, we will form two equations in the form of two variables. After solving, we will get values of x and y and that will be the present age of Nuri and Sonu that we have to find.

Complete step-by-step answer:
Now let us assume the present age of Nuri and Sonu in terms of variables. Let us suppose that the present age of Nuri is x years and the present age of Sonu is y years.
As we are given two time periods, according to which their ages relate. So, let’s use them one by one to obtain two equations.
Five years ago, which means give years in the past their age will become
Age of Nuri five years ago = x - 5 years
Age of Sonu five years ago = y - 5 years
We are given that, Nuri was thrice as old as Sonu five years ago, and hence, we get:
\[\left( x-5 \right)=3\left( y-5 \right)\]
Simplifying and taking variable on outside and constant on other side, we get:
\[\begin{align}
  & x-5=3y-15 \\
 & \Rightarrow x-3y=-10\cdots \cdots \cdots \cdots \left( 1 \right) \\
\end{align}\]
Now, let us solve ages after 10 years.
Ten years later, ages of Sonu and Nuri become
Age of Nuri ten years later = (x+10) years
Age of Sonu ten years later = (y+10) years
We are given that, Nuri's age will be twice as much as age of Sonu ten years later, and hence, we get:
\[x+10=2\left( y+10 \right)\]
Simplifying and taking variable on one side and constant on other side we get:
\[\begin{align}
  & x+10=2y+20 \\
 & \Rightarrow x-2y=10\cdots \cdots \cdots \cdots \left( 2 \right) \\
\end{align}\]
Now, we got two equations in two variables. Let us solve them to find the values of x and y.
Subtracting (1) from (2) we get:
\[\begin{align}
  & x-2y-\left( x-3y \right)=10-\left( -10 \right) \\
 & \Rightarrow x-2y-x+3y=10+10 \\
 & \Rightarrow y=20 \\
\end{align}\]
Putting value of y in (2) we get:
\[\begin{align}
  & x-2\left( 20 \right)=10 \\
 & \Rightarrow x-40=10 \\
 & \Rightarrow x=50 \\
\end{align}\]
Hence, we get x = 50, y = 20
As we have supposed the present age of Nuri as x and Sonu as y. Therefore,
Age of Nuri = 50 years
Age of Sonu = 20 years

Note: Students should note that, while taking age ten years late, we have added ten to x because it was given that we have to take age ten years from present age and not from five years ago. Students can get confused in taking ages from present, past or future, so they should carefully understand the statement first before solving. Students should remember that, ago means taking age in the past and after means taking age in future.