An ordinary Clock becomes 16 minutes fast every day. If it is set right at 9:00 in the morning, then what time will it show at 6:00 in the evening on the same day?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 6:06
1. Calculate the Clock's Rate of Gain
The clock becomes 16 minutes fast every 24 hours.
- Gain per hour = $\frac{16 \text{ minutes}}{24 \text{ hours}}$
- Gain per hour = $\frac{2}{3} \text{ minute}$
2. Calculate the Total Time Elapsed
From 9:00 AM to 6:00 PM on the same day:
- 9:00 AM to 12:00 PM (noon) = 3 hours
- 12:00 PM to 6:00 PM = 6 hours
- Total elapsed time = $3 + 6 = \mathbf{9 \text{ hours}}$
3. Calculate the Total Gain
Multiply the elapsed time by the hourly gain rate:
- Total Gain = $9 \text{ hours} \times \left(\frac{2}{3} \text{ minute/hour}\right)$
- Total Gain = $3 \times 2 = \mathbf{6 \text{ minutes}}$
4. Determine the Time Shown
Since the clock is fast, we add the gain to the actual time:
- Actual Time: 6:00 PM
- Time Shown: $6:00 + 6 \text{ minutes} = \mathbf{6:06}$
Conclusion
At 6:00 in the evening, the clock will show 6:06.