Question

Arjun is twice as old as Shriya five years ago his age was three times Shriya's age. Find their present ages.

Answer 1

Hint: For solving this problem, first let the age of Arjun be x and the age of Shriya be y. Now, by using the age of Arjun and Shriya perform some operation to obtain two relations to link both the ages. By using this methodology, we can easily evaluate the value of x. Hence, by this we can get their present ages.

Complete step-by-step answer:
Let, the age of Arjun be the ‘x’ years.
The age of Shriya is the ‘y’ years.
Now, according to the question, the age of arjun twice when compared with the age of Shriya. This gives us the first relation and we obtain equation (1).
\[x\text{ }=\text{ }2y\text{ }\ldots \text{ }\left( 1 \right)\]
5 years ago,
The age of Arjun = x – 5.
The age of Shriya = y - 5.
According to the question, five years ago Arjun’s age was 3 times the age of Shriya. This gives us the second relation and we obtain equation (2).
\[\begin{align}
  & x-5=3\left( y-5 \right) \\
 & x-5=3y-15 \\
 & x-3y+10=0...(2) \\
\end{align}\]
Putting the value of x from equation (1) in equation (2), we get
$\begin{align}
  & 2y-3y+10=0 \\
 & y=10 \\
\end{align}$
Putting the value of y = 10 in equation (1), the value of x is,
$\begin{align}
  & x=2y \\
 & x=2\times 10 \\
 & x=20 \\
\end{align}$
Hence, the present age of Arjun is 20 years and the present age of Shriya is 10 years.

Note: The key steps involved in solving this problem is the formulation of equations to solve the variables. There are two variables involved, we require two equations. By using the above methodology, we evaluated the ages without any error.