A monkey wanted to climb on the smooth vertical pole of height of 35 metre. In the first one minute he climbs up 5 meter in the next one minute he slips down by 2 metre. Further he repeated the same process till he has reached on the top of the pole. How many times it has to go upward to reach the apex of the pole ?

Options

A. 35
B. 12
C. 11
D. can't say

Answer

To solve the problem of how many times the monkey has to climb upward to reach the top of the 35-meter pole, we can break it down step by step.

### Step-by-Step Solution:

1. **Understanding the Climb and Slip Cycle**:
- In the first minute, the monkey climbs up 5 meters.
- In the second minute, the monkey slips down 2 meters.
- Therefore, in a complete cycle of 2 minutes, the net gain in height is:
\[ \text{Net Gain} = 5 \text{ meters (up)} - 2 \text{ meters (down)} = 3 \text{ meters} \]

2. **Calculating the Effective Height to Climb**:
- The total height of the pole is 35 meters.
- However, we need to consider that the monkey will reach the top with its final upward climb of 5 meters. Thus, we can calculate how much height it needs to cover before the last climb:
\[ \text{Height before last climb} = 35 \text{ meters} - 5 \text{ meters} = 30 \text{ meters} \]

3. **Finding the Number of Cycles Needed**:
- Since the monkey gains 3 meters in each 2-minute cycle, we need to find out how many cycles it takes to climb 30 meters:
\[ \text{Number of cycles} = \frac{30 \text{ meters}}{3 \text{ meters/cycle}} = 10 \text{ cycles} \]

4. **Calculating Total Time Taken**:
- Each cycle takes 2 minutes, so the total time for 10 cycles is:
\[ \text{Total time for cycles} = 10 \text{ cycles} \times 2 \text{ minutes/cycle} = 20 \text{ minutes} \]

5. **Final Climb to Reach the Top**:
- After 20 minutes, the monkey has climbed 30 meters. In the next minute, it will climb the final 5 meters to reach the top of the pole.
- Therefore, the total number of upward climbs is:
\[ \text{Total upward climbs} = 10 \text{ (from cycles)} + 1 \text{ (final climb)} = 11 \]

### Conclusion:
The monkey has to climb upward a total of **11 times** to reach the top of the 35-meter pole.