A watch becomes fast by 5 minutes everyday. By what percent does it become fast?

### Concept & Percentage To find the percentage by which the watch becomes fast, we must compare the time gained to the total time in a standard day. $$\text{Percentage} = \left( \frac{\text{Time Gained}}{\text{Total Standard Time}} \right) \times 100$$ ### Step-by-Step Solution 1. **Find total minutes in a day:** 1 day = 24 hours. 24 hours = $24 \times 60 \text{ minutes} = 1440 \text{ minutes}$. 2. **Identify the gained time:** The watch gains 5 minutes in this 1440-minute period. 3. **Calculate the percentage:** $$\text{Percentage} = \left( \frac{5}{1440} \right) \times 100$$ $$\text{Percentage} = \frac{500}{1440}$$ Simplify the fraction by dividing numerator and denominator by 10: $$\text{Percentage} = \frac{50}{144}\%$$ ### Exam Strategy & Shortcut Instead of fully reducing the fraction to lowest terms (which would be $\frac{25}{72}$), glance at the options first. The option (d) leaves the fraction partially unreduced at $\frac{50}{144}$, saving you an extra calculation step. ### Common Pitfall A common mistake is using 24 hours as the denominator without converting the numerator to hours, resulting in $\frac{5}{24}\%$. Units must match! ### Final Answer Therefore, the correct answer is **$\frac{50}{144}\%$**.