The ratio of present ages of Rehana and her mother is 2 : 7. After 2 years, the ratio of their ages will be 1 : 3. What is Rehana's present age ?

Let the present ages of Rehana and her mother be 2x years and 7x years, respectively.

After 2 years,

Age of Rehana = (2x + 2) years

Age of Rehana's mother = (7x + 2) years

It is given that after 2 years, the ratio of their ages will be 1 : 3.

$$\begin{gathered} \therefore \frac{2x+2}{7x+2}=\frac{1}{3} \\ \Rightarrow 6x+6=7x+2 \\ \Rightarrow 7x-6x=6-2 \\ \Rightarrow x=4 \end{gathered}$$
∴ Rehana's present age = 2x = 2 × 4 = 8 years

Thus, the present age of Rehana is 8 years.