A fraction becomes $\displaystyle \frac{1}{3}$ when $\displaystyle 1$ is subtracted from the numerator. It becomes $\displaystyle \frac{1}{4}$ when $\displaystyle 8$ is added to the denominator. Find the fraction.

Let the fraction be \(\displaystyle \frac{\boldsymbol{x}}{\boldsymbol{y}}\) \[\begin{aligned} & \frac{x-1}{y}=\frac{1}{3} \Rightarrow 3 x-y=3 \\ & \frac{x}{y+8}=\frac{1}{4} \Rightarrow 4 x-y=8 \end{aligned} \] Solving to get \(\displaystyle \mathrm{x}=5, \mathrm{y}=12\) Fraction is \(\displaystyle \frac{\mathbf{5}}{\mathbf{1 2}}\)