Question

Ben is $4$ times as old as Ishaan. $6$ years ago, Ben was $6$ times as old as Ishaan. How old is Ishaan now?

Answer 1

Step 1: Find the age of Ben in terms of $x.$

Let the age of Ishaan be $x.$

It is given that Ben is $4$ times as old as Ishaan.

Thus, the age of Ben is $4x.$

Step 2: Find the value of $x.$

It is also given that $6$ years ago, Ben was $6$ times as old as Ishaan. Therefore,

$$\begin{gathered} 4x-6=6\left(x-6\right) \\ \Rightarrow 4x-6=6x-36 \\ \Rightarrow 4x-6x=-36+6 \\ \Rightarrow -2x=-30 \\ \Rightarrow x=\frac{-30}{-2} \\ \therefore x=15 \end{gathered}$$

Hence, the age of Ishaan is $15$ years.