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

Solution(By Examveda Team)

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