The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes $\frac{1}{2}$. Find the fraction.

Given:

The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes $\frac{1}{2}$. 

 To do:

We have to find the original fraction.

Solution:

Let the denominator of the original fraction be $x$.

This implies,

The numerator of the original fraction$=12-x$.

The original fraction$=\frac{12-x}{x}$.

When the denominator is increased by 3, the fraction becomes $\frac{1}{2}$

This implies,

New fraction$=\frac{12-x}{x+3}$

According to the question,

$\frac{12-x}{x+3}=\frac{1}{2}$

$2(12-x)=1(x+3)$

$24-2x=x+3$

$x+2x=24-3$

$3x=21$

$x=\frac{21}{3}$

$x=7$

$\Rightarrow 12-x=12-7=5$.

Therefore, the original fraction is $\frac{5}{7}$.  

Tutorialspoint

Updated on: 10-Oct-2022

73 Views

Kickstart Your Career

Get certified by completing the course

Get Started