Question 32

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 ?

Solution

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)

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