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
$\frac{x+3}{y+3}=\frac{3}{4}$
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
$3+y=8$
$\Rightarrow y=5$
Hence the fraction is $\frac{x}{y}=\frac{3}{5}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.