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.

Let's consider the fraction is $\frac{P}{Q}$ First, when 1 is subtracted from numerator, then: $\frac{P - 1}{Q}$ = $\frac{1}{3}$ ∴ 3 (P -1) = Q ∴ 3P - Q = 3 ............... (i) Next, when 8 is added to the denominator, then: $\frac{P}{Q + 8}$ = $\frac{1}{4}$ ∴ 4 P = Q + 8 ∴ 4 P - Q = 8 .............. (ii) By solving equation (i) and equation (ii), we get: P = 5 and Q = 12 Therefore, the fraction is $\frac{5}{12}$.

A fraction becomes 1/3 when 1 is subtracted from the numerator

Q) A fraction becomes $A fraction becomes 1/3 when 1$ when 1 is subtracted from the numerator. It becomes $A fraction becomes 1/3 when 1$ when 8 is added to the denominator. Find the fraction.