A monkey wanted to climb on the smooth vertical pole of height of 35 metre. In the first one minute he climbed up 5 metre in the next on minute he slipped down by 2 metre. Further he repeated the same process till he had reached on the top of the pole: If the height of the pole is 36 metre then the time taken by monkey to reach at the top of the pole is:

Options

A. 22 min. 36 sec
B. 22 min. 24 sec
C. 23 min.12 sec
D. none of these

Answer

To solve the problem of how long it takes the monkey to climb to the top of a 36-meter pole, we can break down the monkey's climbing and slipping process step by step.

### Step-by-Step Solution:

1. **Understanding the Climb and Slip Pattern:**
- In the first minute, the monkey climbs up 5 meters.
- In the second minute, the monkey slips down 2 meters.
- Therefore, in 2 minutes, the net gain in height is \(5 - 2 = 3\) meters.

2. **Calculating the Effective Height after Each Cycle:**
- Each cycle of 2 minutes results in a net gain of 3 meters.
- We need to determine how many such cycles are required to get close to the top of the pole (36 meters).

3. **Finding the Number of Cycles:**
- After 2 minutes, the monkey climbs to 3 meters.
- After 4 minutes, the monkey climbs to \(3 + 3 = 6\) meters.
- After 6 minutes, the monkey climbs to \(6 + 3 = 9\) meters.
- Continuing this pattern:
- After 8 minutes: 12 meters
- After 10 minutes: 15 meters
- After 12 minutes: 18 meters
- After 14 minutes: 21 meters
- After 16 minutes: 24 meters
- After 18 minutes: 27 meters
- After 20 minutes: 30 meters
- After 22 minutes: 33 meters
- After 24 minutes: 36 meters

4. **Reaching the Top:**
- At the end of 24 minutes, the monkey reaches exactly 36 meters.
- Since the monkey climbs up 5 meters in the first minute of the cycle and does not slip back after reaching the top, the monkey reaches the top in 24 minutes.

### Conclusion:
The time taken by the monkey to reach the top of the 36-meter pole is **24 minutes**.