A number is mistakenly divided by 4 instead of multiplying by 4. What the percentage change in the result due to this mistake?

Correct Option

Let the original number be represented by 'x'.

• The actual intended result of the operation was 4 multiplied by the number, which is 4x.
• The mistaken result, due to division by 4, is x/4.
• To determine the change in the result, the difference between the actual and mistaken results is calculated: $$4x-\frac{x}{4}=\frac{16x-x}{4}=\frac{15x}{4}$$
• The percentage change is calculated relative to the actual intended result: $$\frac{\text{Change}}{\text{Actual Result}}\times 100=\frac{\frac{15x}{4}}{4x}\times 100$$ $$=\frac{15x}{16x}\times 100=\frac{15}{16}\times 100=0.9375\times 100=93.75\mathrm{\%}$$

Therefore, the percentage change in the result due to the mistake is 93.75%.

Incorrect Options

Options 1 (25%), 2 (72.75%), and 3 (50%) are incorrect as they do not correspond to the accurate calculation of the percentage change based on the given problem statement. The correct calculation, as demonstrated above, yields 93.75%.