A monkey wants to climb up a pole of 50 metre height. He first climbs up 1 metre but he falls back by the same height. Again he climbs up 2 metre but he falls back by 1 metre. Once again he climbs up 3 metre but he falls back by 1 metre. Again he climbs up 4 metre but he falls back be 1 metre. In this way he reaches at the top of the pole. If it is known that the monkey needs 10 seconds for 1 metre in upward direction , then the total time required by monkey to reach at the top of the pole. For your kind information it must be clear to you that when he will reach on the top, he will not be slip back. The total time required by this monkey to reach on the top of the poll is:

Options

A. 9 minutes 10 seconds
B. 10 minutes
C. 8 minutes 20 seconds
D. none of these

Answer

To solve the problem of the monkey climbing the 50-meter pole, we will break down the monkey's climbing pattern and calculate the total time taken to reach the top.

### Step-by-Step Solution:

1. **Understand the Climbing Pattern**:
- The monkey climbs 1 meter and falls back 1 meter.
- Then, he climbs 2 meters and falls back 1 meter.
- Next, he climbs 3 meters and falls back 1 meter.
- Finally, he climbs 4 meters and falls back 1 meter.
- This pattern continues until he reaches the top of the pole.

2. **Calculate Effective Climb for Each Attempt**:
- For the first climb (1 meter up, 1 meter down): Net gain = 0 meters.
- For the second climb (2 meters up, 1 meter down): Net gain = 1 meter.
- For the third climb (3 meters up, 1 meter down): Net gain = 2 meters.
- For the fourth climb (4 meters up, 1 meter down): Net gain = 3 meters.
- This pattern continues, where each climb adds an increasing amount to the net gain.

3. **Identify the Climbing Sequence**:
- The monkey's effective gains can be summarized as follows:
- After 1st climb: 0 meters
- After 2nd climb: 1 meter
- After 3rd climb: 3 meters (1 + 2)
- After 4th climb: 6 meters (3 + 3)
- After 5th climb: 10 meters (6 + 4)
- After 6th climb: 15 meters (10 + 5)
- After 7th climb: 21 meters (15 + 6)
- After 8th climb: 28 meters (21 + 7)
- After 9th climb: 36 meters (28 + 8)
- After 10th climb: 45 meters (36 + 9)
- After 11th climb: 55 meters (45 + 10)

4. **Determine When the Monkey Reaches the Top**:
- The monkey reaches the top of the pole (50 meters) during the 11th climb when he climbs 10 meters.
- At this point, he reaches 55 meters but does not fall back since he has reached the top.

5. **Calculate Total Time Taken**:
- Each meter takes 10 seconds.
- The monkey climbs a total of:
- 1 meter (1st climb) + 2 meters (2nd climb) + 3 meters (3rd climb) + ... + 10 meters (11th climb).
- This is the sum of the first 11 natural numbers:
\[ \text{Total Climb} = 1 + 2 + 3 + ... + 10 = \frac{n(n + 1)}{2} = \frac{10(10 + 1)}{2} = 55 \text{ meters} \]
- Total time taken = Total meters climbed × Time per meter = 55 meters × 10 seconds/meter = 550 seconds.

### Final Answer:
The total time required by the monkey to reach the top of the pole is **550 seconds**.