A man starts climbing a 11 m high wall at 5 pm. In each minute he climbs up 1 m but slips down 50 cm. At what time will he climb the wall?

Options

A. `5:30 ` pm
B. `5:21 ` pm
C. `5:25 ` pm
D. `5:27` pm

Answer

To solve the problem step by step, we need to calculate how long it will take for the man to climb the 11-meter high wall, considering he climbs up 1 meter each minute but slips down 0.5 meters (or 50 cm) in the same time.

### Step-by-Step Solution:

1. **Identify the Effective Climb per Minute:**
- The man climbs 1 meter in one minute but slips down 0.5 meters.
- Therefore, the effective height climbed in one minute is:
\[ \text{Effective climb} = \text{Climb} - \text{Slip} = 1 \text{ m} - 0.5 \text{ m} = 0.5 \text{ m} \]

2. **Calculate the Total Height to Climb:**
- The total height of the wall is 11 meters.

3. **Determine How Many Minutes to Reach Near the Top:**
- Since the man climbs 0.5 meters effectively each minute, we need to find out how many minutes it will take to reach just below the top of the wall:
\[ \text{Height to reach before the last climb} = 11 \text{ m} - 1 \text{ m} = 10 \text{ m} \]
- Now, calculate the time taken to climb 10 meters:
\[ \text{Time} = \frac{\text{Height}}{\text{Effective climb}} = \frac{10 \text{ m}}{0.5 \text{ m/min}} = 20 \text{ minutes} \]

4. **Final Climb to the Top:**
- After 20 minutes, the man will have climbed 10 meters. In the next minute, he will climb the last meter to reach the top of the wall without slipping back down since he will reach the top at the end of that minute.

5. **Total Time Taken:**
- Total time taken to climb the wall:
\[ \text{Total time} = 20 \text{ minutes} + 1 \text{ minute} = 21 \text{ minutes} \]

6. **Determine the Final Time:**
- The man starts climbing at 5 PM. Adding 21 minutes to this time gives:
\[ 5:00 \text{ PM} + 21 \text{ minutes} = 5:21 \text{ PM} \]

### Conclusion:
The man will reach the top of the wall at **5:21 PM**.

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