101
A fraction becomes $\frac{1}{3}$ when $1$ is subtracted from the numerator. It becomes $\frac{1}{4}$ when $8$ is added to the denominator. Find the fraction.
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Let the fraction be $\frac{x}{y}$
$\frac{x-1}{y} = \frac{1}{3} \implies 3x - y = 3$
$\frac{x}{y+8} = \frac{1}{4} \implies 4x - y = 8$
Solving to get $x = 5, y = 12$
Fraction is $\frac{5}{12}$
$\frac{x-1}{y} = \frac{1}{3} \implies 3x - y = 3$
$\frac{x}{y+8} = \frac{1}{4} \implies 4x - y = 8$
Solving to get $x = 5, y = 12$
Fraction is $\frac{5}{12}$