Question

The ratio of present ages of Veena and Kinjal is $2:3$. The ratio of ages of Veena after $4$ years and the age of Kinjal $4$ years before is $4:1$. Find their present ages.

Answer 1

Let $x$ and $y$ be the present ages of Veena and Kinjal.

According to the question-

$\frac{x}{y}=\frac{2}{3}$

$\Rightarrow x=\frac{2}{3}y.....\left(1\right)$

Also, given that ratio of ages of Veena after $4$ years and the age of Kinjal $4$ years before is $4:1$, i.e.,

$\frac{x+4}{y-4}=\frac{4}{1}$

$\Rightarrow x+4=4(y-4)$

$\Rightarrow \frac{2}{3}y+4=4y-16$

$\Rightarrow 4y-\frac{2}{3}y=16+4$

$\Rightarrow \frac{10}{3}y=20$

$\Rightarrow y=20\times \frac{3}{10}=6$ years

Substituting the value of $y$ in equation $\left(1\right)$, we have

$x=\frac{2}{3}\times 6=4$ years.

Hence the present ages of Veena and Kinjal are $4$ and $6$ years respectively.