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

Explanation

Let fraction be $$x$$ Ram's correct answer should be = $$\frac{7}{8}x$$ Ram's actual answer = $$\frac{x}{\frac{7}{8}}=\frac{8}{7}x$$ Difference = $$\frac{8x}{7}-\frac{7x}{8}=\frac{75}{784}$$ => $$\frac{(64x-49x)}{56}=\frac{75}{784}$$ => $$15x=\frac{75}{784}\times56$$ => $$x=\frac{75}{14}\times\frac{1}{15}$$ => $$x=\frac{5}{14}$$ $$\therefore$$ Ram's correct answer should be = $$\frac{7}{8}\times\frac{5}{14}=\frac{5}{16}$$ => Ans - (C)