The sum of the numerator and the denominator


The sum of the numerator and the denominator of a fraction is 8 . If 3 is added to both the numerator and the denominator, the fraction becomes $\frac{3}{4}$. Find the fraction.


Here we are assuming that numerator and denominator are $x$ and $y$ respectively, then fraction will be $\frac{x}{y}$ and we have to find the value of $\frac{x}{y}$.

From the given condition,

x + y = 8…… (1)

If 3 are added in numerator and denominator then fraction will be $\frac{3}{4}$, from this we have


Now, multiply the equation (1) by 3, we get

3x + 3y = 24…… (3)

Now we take the addition of equations (2) and (3), we get

$7 x=21$

$\Rightarrow x=3$

Put the value of x in the equation (1), we have


$\Rightarrow y=5$

Hence the fraction is $\frac{x}{y}=\frac{3}{5}$

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