Question

Arjun is twice as old as Shreya five years ago his age was three times Shreya’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 Shreya be y. Now, by using the age of Arjun and Shreya perform some operations 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 solution:
Let, the age of Arjun be the ‘x’ years and the age of Shreya is the ‘y’ years.
Now, according to the question, the age of Arjun is twice when compared with the age of Shreya. This gives us the first relation and we obtain equation (1).
$ \Rightarrow x = 2y$..............….. (1)
5 years ago,
The age of Arjun was $\left( {x - 5} \right)$ years.
The age of Shreya was $\left( {y - 5} \right)$ years.
According to the question, five years ago Arjun’s age was 3 times the age of Shreya. This gives us the second relation and we obtain equation (2).
$ \Rightarrow x - 5 = 3\left( {y - 5} \right)$
Multiply the terms on the right side,
$ \Rightarrow x - 5 = 3y - 15$
Move variable part on one side and constant part on another side,
$ \Rightarrow x - 3y = - 10$.............….. (2)
Putting the value of x from equation (1) in equation (2), we get
$ \Rightarrow 2y - 3y = - 10$
Subtract the terms on the left side,
$ \Rightarrow - y = - 10$
Cancel out common terms on both sides,
$ \Rightarrow y = 10$
Putting the value of y = 10 in equation (1), the value of x is,
$ \Rightarrow x = 2 \times 10$
Multiply the term,
$ \Rightarrow x = 20$

Hence, the present age of Arjun is 20 years and the present age of Shreya 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.