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?

6:06

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.