If 3 is added to the denominator of a fraction, it becomes 1/3 and if 4 be added to its numerator, It becomes 3/4, then fraction is?

Let the required fraction be p/q
∵ p / (q + 3) = 1/3
⇒ 3p - q = 3 ...(i)
and, (p + 4) / q = 3/4
⇒ 4p - 3q = -16 ...(ii)
Solving these equations, we get p = 5, q = 12
∴ Required fraction = 5/12