Question

The sum of numeretor and deniminator of a faction 4 more than its numerator If $3$ is added to numerator and denominator, its ratio becomes $2:3$. Find the fraction

Answer 1

Let numerator and denominator be $x$ and $y.$

According to first condition,

$\Rightarrow$ $x+y=4+x$

$\therefore$ $y=4$

According to second condition,

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

$\Rightarrow$ $\frac{x+3}{4+3}=\frac{2}{3}$ [ Substituting value of $y$ ]

$\Rightarrow$ $\frac{x+3}{7}=\frac{2}{3}$

$\Rightarrow$ $x+3=\frac{14}{3}$

$\Rightarrow$ $x=\frac{14}{3}-3$

$\Rightarrow$ $x=\frac{14-9}{3}$

$\Rightarrow$ $x=\frac{5}{3}$

$\Rightarrow$ Required fraction $=\frac{x}{y}=\frac{\frac{5}{3}}{4}=\frac{5}{12}$