A fraction becomes $\frac{1}{3}$ when $2$ is subtracted from the numerator and it becomes $\frac{1}{2}$ when $1$ is subtracted from the denominator. Find the fraction.

Given: A fraction becomes $\frac{1}{3}$ when $2$ is subtracted from the numerator and it becomes $\frac{1}{2}$ when $1$ is subtracted from the denominator

To do: To find the fraction.

Solution:

Let $\frac{x}{y}$ be the fraction.

On subtracting 2 from the numerator,

$\frac{x-2}{y}=\frac{1}{3}$


$\Rightarrow3x-6=y$

$\Rightarrow3x-y=6 $            ..............$( 1)$


On subtracting 1 from the denominator,

$\frac{x}{y-1}=\frac{1}{2}$

$\Rightarrow2x=y-1$

$\Rightarrow2x-y=-1 $         ................$( 2)$

On subtracting $( 2)$ from $( 1)$,

$3x-y-2x+y=6+1$

$\Rightarrow x=7$

On subtuting $x=7$ in $( 1)$

$3(7)-y=6$

$\Rightarrow y=21-6$

$\Rightarrow y=15$ 

Therefore the fraction $=\frac{x}{y}=\frac{7}{15}$.
 

Updated on: 10-Oct-2022

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