Question

A fraction becomes $\frac{1}{3}$ when $1$ is subtracted from the numerator and it becomes $\frac{1}{4}$ when $8$ is added to its denominator. The fraction obtained is:

Answer 1

Let's find the fraction.

Let the fraction be $\frac{p}{q}$

Given that,

$$\begin{gathered} \frac{\left(p-1\right)}{q}=\frac{1}{3} \\ 3(p-1)=q \\ 3p-3=q \\ 3p-q=3\to \left(1\right) \end{gathered}$$

Also, given,

$$\begin{gathered} \frac{p}{(q+8)}=\frac{1}{4} \\ 4p=q+8 \\ 4p-q=8\to \left(2\right) \end{gathered}$$

By solving equation $\left(1\right)\mathrm{and}\left(2\right)$ we get;

$p=5,q=12$

Therefore, the required fraction is $\frac{5}{12}$