Ram was asked to find $\frac{7}{8}$ of a fraction but he mistakenly divided the fraction by $\frac{7}{8}$. As a result, the difference between the answers was $\frac{75}{784}$. What should be Ram’s correct answer?

Let the required fraction be $x$.
The correct calculation should have been: $\frac{7}{8}\times x=\frac{7x}{8}$
The mistaken calculation performed was: $x÷\frac{7}{8}=\frac{8x}{7}$

According to the question, the difference between the results is $\frac{75}{784}$:

$$\frac{8x}{7}-\frac{7x}{8}=\frac{75}{784}$$

Taking the LCM of the denominators ($7$ and $8$), which is $56$:

$$\frac{64x-49x}{56}=\frac{75}{784}$$

$$\frac{15x}{56}=\frac{75}{784}$$

$$x=\frac{75}{784}\times \frac{56}{15}$$

Simplifying the expression:

$$\frac{75}{15}=5$$

$$\frac{784}{56}=14$$

$$x=\frac{5}{14}$$

The original fraction is $\frac{5}{14}$. Now, find Ram's correct answer, which is $\frac{7}{8}$ of the fraction:

$$\text{Correct Answer}=\frac{7}{8}\times \frac{5}{14}=\frac{5}{8\times 2}=\frac{5}{16}$$