Question

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

Answer 1

Let the numerator be x , denominator be y so the given fraction is $\frac{x}{y}$
Given that the sum of the numerator and denominator of a fraction is 8.

$\to x+y=8$.....(1)
$\to x=y-8$

When 3 is added to the numerator and the denominator the fraction becomes
$\frac{(x+3)}{(y+3)}$ =$\frac{3}{4}$ ....(2)

$\to 4x+12=3y+9$
$\to 4(8-y)+12-3y-3=0$
$\to 32+3-7y=0$

$\to y=5$
$\to x=3$
Hence aubstituting the value of x and y in the fraction above we have
$x/y=3/5$