Question:
Rakhi's mother is four times as old as Rakhi. After 5 years, her mother will be three times as old as she will be then. Find their present ages.
Solution:
Let the present age of Rakhi be $\mathrm{x}$.
Then, the present age of Rakhi's mother will be $4 \mathrm{x}$.
After five years, Rakhi 's age will be $(\mathrm{x}+5)$.
After five years, her mother's age will be $(4 \mathrm{x}+5)$.
$4 x+5=3(x+5)$
$\Rightarrow 4 x+5=3 x+15$
$\Rightarrow 4 x-3 x=15-5$
$\Rightarrow x=10$
Present age of Rakhi $=10$ years
Present age of Rakhi's mother $=4(\mathrm{x})=4 \times 10=40$ years