By mistake, the reciprocal of a positive fraction got…

In the following passage, some words have been deleted. Fill in the blanks with the help of the alternatives given. Select the most appropriate option for each blank.
Moore worked without stopping until eleven o’clock. Then he made (1)______ a cup of tea. He was enjoying himself sitting alone (2)______ the fireside. The firelight danced on the walls and (3)______ strange shadows around the room. His tea tasted (4)______ and there was nobody to disturb him. Then, for (5)______ first time he noticed how much noise the rats were making.

By mistake, the reciprocal of a positive fraction got typed in place of itself, and thereby its value got reduced by $\frac{175}{4}$ %.

What was the value of the fraction ?

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. $\frac{4}{3}$

Let the original number be x.

The reciprocal of the original number = 1/x

According to the question -

x - 1/x = 175x/400

(x² - 1)/x = 175/400

400(x² - 1) = 175x²

400x² - 400 = 175x²

x² = 400/225

x = 20/15 = 4/3

SSC CGL 2021 PYQ — Question 75