Question

The numerator of a rational number is less than its denominator by $3.$ If $5$ is added to both its numerator and its denominator then it becomes $\frac{3}{4}$ Find the numbers.

Answer 1

Let the rational number be $\frac{x}{y}$

In this the numerator is $x$ and denominator is $y$

Given $x$ is less than $y$ by $3$

$⟹x+3=y$

And also if $5$ is added to both $x$ and $y$ then it will become

$\frac{3}{4}$

$⟹\frac{x+5}{y+5}=\frac{3}{4}$

$⟹4x+20=3y+15$

$⟹4x+20=3(x+3)+15$

$⟹4x+20=3x+24$

$⟹x=4,y=x+3=4+3=7$

The number is $\frac{4}{7}$