A number is mistakenly divided by 4 instead of multiplying by 4. What is the percentage change in the result due to this mistake?
- (a) 25%
- (b) 50%
- (c) 72·75%
- (d) 93·75% ✓ UPSC's answer
Why the answer is (d)
• Let the number be x. The correct result is 4x; the mistaken result is x/4.
• The result falls by 4x − x/4 = 15x/4.
• As a percentage of the correct result: (15x/4) ÷ 4x × 100 = 15/16 × 100 = 93.75%.
• Option (d).
Why the other options are wrong
- (a) 25%
- 25% is 1/4 of the correct result, but the mistake reduces the result from 4x to x/4 — a fall of 15/16, i.e. 93.75%.
- (b) 50%
- 50% does not match: the result falls from 4x to x/4, which is 93.75% of 4x.
- (c) 72·75%
- 72.75% does not match: (4x − x/4) ÷ 4x = 15/16 = 93.75%.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.