Question

Ritu is now four times as old as his brother Raju.

In $4$years time, her age will be twice Raju's age.

What are their present ages?

Answer 1

Step 1: The present ages of Ritu and Raju

Let the present age of Raju be $x$ years.

It is given that the age of Ritu is four times the age of Raju

$\Rightarrow$Age of Ritu$=4\times x$ years

Step 2: Age of Ritu and Raju after $4$ years

After $4$ years,

Age of Raju$=(x+4)$years

Age of Ritu $=(4x+4)$ years

Step 3: Finding the present ages of Ritu and Raju

It is given that after four years, Ritu's age will be twice that of Raju's age

$$\begin{gathered} \Rightarrow 4x+4=2(x+4) \\ \Rightarrow 4x+4=2x+8 \\ \Rightarrow 4x–2x=8–4 \\ \Rightarrow 2x=4 \\ \Rightarrow x=\frac{4}{2} \\ \Rightarrow x=2 \end{gathered}$$

$\Rightarrow$Ritu's present age$=4x=4\times 2=8$years

Therefore, Raju's present age is $2$ years and Ritu's present age is $8$ years.