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 original number be $x$.

• The correct operation is multiplication by 4, so the correct result is $4x$.

• The mistaken operation is division by 4, so the incorrect result is $x/4$.

• The absolute difference between the correct and incorrect results is $4x - x/4 = 15x/4$.

• The percentage change is calculated relative to the correct result: $(15x/4) / 4x \times 100$.

• This simplifies to $15/16 \times 100 = 93.75\%$, which matches option (d).

Why the other options are wrong

(a) 25%: 25% is the reciprocal of 4, not the percentage difference between $4x$ and $x/4$.
(b) 50%: 50% is an arbitrary value that does not correspond to the ratio of the difference to the correct result.
(c) 72·75%: 72.75% is incorrect; the correct calculation yields 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.