Question

The sum of a numerator and denominator of a fraction is 18. If the denominator is increased by 2, the fraction reduces to 1/3. Find the fraction.

Answer 1

Let the numerator is x

And denominator is y

As per the question $x+y=18$ .......(1)

And $\frac{x}{y+2}=\frac{1}{3}$ .........(2)

From (1) and (2), we get

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

$\Rightarrow 54-3y=y+2$

$\Rightarrow 52=4y$

$\Rightarrow y=13$

And $x=18-13$

$\Rightarrow x=5$

So, the fraction is: $\frac{5}{13}$