If the numerator of a fraction is increased by 1/4 and the denominator is decreased byy 1/3 , the new fraction obtained is 33/64 . What was the original fraction ?

Answer: Option D

Let the fraction be $$\frac{x}{y}$$
Then,
$$\begin{array}{rl}& \iff \frac{x+\frac{1}{4}}{y-\frac{1}{3}}=\frac{33}{64}\\ & \iff \frac{3\left(4x+1\right)}{4\left(3y-1\right)}=\frac{33}{64}\\ & \iff \frac{4x+1}{3y-1}=\frac{33}{64}\times \frac{4}{3}\\ & \iff \frac{4x+1}{3y-1}=\frac{11}{16}\\ & \iff 16\left(4x+1\right)=11\left(3y-1\right)\\ & \iff 64x+16=33y-11\\ & \iff 64x-33y=-27\end{array}$$
Which cannot be solved to find $$\frac{x}{y}$$
Hence, the original fraction cannot be determined from the given data.