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: the minimum time required for this job is :

Options

A. 21 minute
B. 22 minute
C. 24 minute
D. none of these

Answer

To solve the problem of how long it takes for the monkey to climb to the top of a 35-meter pole, we can break it down step by step.

### Step 1: Understand the climbing and slipping process
The monkey climbs 5 meters in the first minute and then slips down 2 meters in the next minute. This means that in every 2 minutes, the net gain in height is:

\[ \text{Net gain} = \text{Climb} - \text{Slip} = 5 \text{ meters} - 2 \text{ meters} = 3 \text{ meters} \]

### Step 2: Calculate the height reached after several cycles
Since the monkey gains 3 meters every 2 minutes, we need to find out how many cycles it takes to reach close to 35 meters.

Let’s calculate how many complete cycles (2 minutes each) it takes to get close to 35 meters without exceeding it.

- After 2 minutes: 3 meters
- After 4 minutes: 6 meters
- After 6 minutes: 9 meters
- 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

At the end of 22 minutes, the monkey is at 33 meters.

### Step 3: Climb the final distance
Now, the monkey is at 33 meters and needs to climb the remaining distance to reach the top of the pole (35 meters). In the next minute (23rd minute), the monkey climbs 5 meters, reaching 38 meters. However, since the pole is only 35 meters tall, the monkey will reach the top before slipping back.

### Step 4: Calculate total time
- The monkey takes 22 minutes to reach 33 meters.
- In the 23rd minute, the monkey climbs to 35 meters and reaches the top.

Thus, the total time taken for the monkey to reach the top of the pole is:

\[ \text{Total time} = 22 \text{ minutes} + 1 \text{ minute} = 23 \text{ minutes} \]

### Final Answer
The minimum time required for the monkey to reach the top of the pole is **23 minutes**.

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