A monkey while trying to reach the top of a pole of height 12 meters takes every time a jump of 2 meters but slips 1 meter while holding the pole. The number of jumps required to reach the top of the pole, is:

Options

A. 6
B. 10
C. 11
D. 12

Answer

To solve the problem of how many jumps the monkey needs to reach the top of a 12-meter pole, we can break it down step by step.

### Step-by-Step Solution:

1. **Understand the Jump and Slip Mechanism:**
- The monkey jumps up 2 meters but slips back 1 meter after each jump.
- Therefore, the net gain in height after each jump is \(2 - 1 = 1\) meter.

2. **Calculate the Effective Height After Each Jump:**
- After the first jump, the monkey reaches \(2\) meters but slips back to \(1\) meter.
- After the second jump, the monkey reaches \(3\) meters but slips back to \(2\) meters.
- Continuing this pattern, after \(n\) jumps, the monkey will have effectively gained \(n\) meters.

3. **Determine When the Monkey Reaches the Top:**
- The monkey will continue this pattern until he reaches a height where he can jump to the top without slipping back.
- If the monkey jumps for \(n\) times, he will reach a height of \(n\) meters after slipping back.
- On the \(11^{th}\) jump, the monkey jumps to \(11 + 2 = 12\) meters, reaching the top of the pole.

4. **Final Calculation:**
- Therefore, the monkey will reach the top of the pole after \(11\) jumps.

### Conclusion:
The number of jumps required for the monkey to reach the top of the pole is **11 jumps**.

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