The sum of a numerator and denominator of a fraction is 18. If the denominator is increased by 2, the fraction reduces to $\frac{1}{3}$. Find the fraction.

Given:

The sum of a numerator and denominator of a fraction is 18. If the denominator is increased by 2, the fraction reduces to $\frac{1}{3}$.

 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$=18-x$.

The original fraction$=\frac{18-x}{x}$.

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

This implies,

New fraction$=\frac{18-x}{x+2}$

According to the question,

$\frac{18-x}{x+2}=\frac{1}{3}$

$3(18-x)=1(x+2)$

$54-3x=x+2$

$x+3x=54-2$

$4x=52$

$x=\frac{52}{4}$

$x=13$

$\Rightarrow 18-x=18-13=5$.

Therefore, the original fraction is $\frac{5}{13}$.   

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Updated on: 10-Oct-2022

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