Question

A clock is set right at 10 am.The clock gains 10 minutes in a day.What will be the true time when the watch indicates 3 pm the next day?

• A. 12 minutes past 2 pm
• B. 45 minutes past 2 pm
• C. 32 minutes past 2 pm
• D. 48 minutes past 2 pm

Answer 1

The Correct Option is D

To find the true time when the watch indicates 3 pm the next day, we need to determine how much the clock will gain by the time it shows 3 pm the following day.

The clock is set right at 10 am initially and gains 10 minutes in a 24-hour period. This means each day has 24 actual hours, but the clock records 24 hours and 10 minutes. Let's calculate the time duration involved:

1. Calculate duration from 10 am Day 1 to 3 pm Day 2:
   • From 10 am to 3 pm the next day is 29 hours.
2. Calculate the time recorded by the clock:
   • Since the clock gains 10 minutes over 24 hours, the clock runs for more time than actual:
   • Actual Time: 24 hours
   • Clock Time: 24 hours + 10 minutes
   • So, for every 24 hours, the clock records 24 hours and 10 minutes. 
   • Hence, the time shown by the clock after 29 actual hours can be calculated using proportion:
   • \(\frac{{24 \text{ hrs } + 10 \text{ mins}}}{24 \text{ hrs}} = \frac{x}{29 \text{ hrs}}\)
   • Solve for x:
   • \(x = \frac{29 \times (24 \text{ hrs } + \frac{10}{60} \text{ hrs})}{24}\)
   • \(x = \frac{29 \times (1440 + 10)}{1440} \text{ mins}\)
   • \(x = \frac{29 \times 1450}{1440} \text{ mins}\)
   • \(x = \frac{42050}{1440} \text{ mins}\)
   • \(x \approx 29 \text{ hours and } 10 \text{ minutes}\)
3. Conclusion:
   • Thus, the watch will show 29 hours and 10 minutes when the true time has elapsed 29 hours.
   • This means that when the watch shows "3 pm" on the next day (29 hours), the actual time would be 29 hours - 20 minutes = 28 hours and 40 minutes.
   • Counting back from 3 pm, 20 minutes leads us back to 2 hours and 48 minutes past 12 pm.

Therefore, the true time when the watch indicates 3 pm the next day is 48 minutes past 2 pm. This matches with the option '48 minutes past 2 pm'.

Answer 2

The clock gains 10 minutes in 24 hours, so in 24 hours, the clock will show 10 minutes more than the true time. Since the time is being observed after 1 day and 5 hours (from 10 am to 3 pm next day), we calculate the total time elapsed:

\[ 24 \, \text{hours} + 5 \, \text{hours} = 29 \, \text{hours}. \]

The clock gains 10 minutes for every 24 hours, so in 29 hours, it will gain:

\[ \frac{10 \times 29}{24} = 12.08 \, \text{minutes}. \]

Thus, when the watch shows 3 pm, the true time is:

\[ 3 : 00 - 12.08 \, \text{minutes} = 2 : 47 : 52 \, \text{pm}. \]

So, the true time is approximately 48 minutes past 2 pm.