A drunkard is walking along a stsraight road. He takes five steps forward and three steps backward and so on. Each step is `1 m` long and takes `1 s`. There is a pit on the road `11 m`, away from the starting point. The drunkard will fall into the pit after.

Options

A. ` 29 s`
B. ` 21 s`
C. ` 37 s`
D. ` 31 s`

Explanation

To solve the problem of the drunkard walking along a straight road and falling into a pit, we can break it down step by step.

### Step-by-Step Solution:

1. **Understanding the Movement Pattern**:
- The drunkard takes 5 steps forward and then 3 steps backward.
- Each step is 1 meter long and takes 1 second.

2. **Calculating the Net Movement in One Cycle**:
- In one complete cycle (5 steps forward and 3 steps backward):
- Forward movement: 5 meters
- Backward movement: 3 meters
- Net movement = 5 - 3 = 2 meters
- Time taken for one cycle = 5 seconds (forward) + 3 seconds (backward) = 8 seconds

3. **Finding the Number of Cycles to Reach Near the Pit**:
- The pit is located 11 meters away from the starting point.
- We need to determine how many complete cycles the drunkard can perform before reaching or exceeding 11 meters.
- After 4 cycles:
- Total distance covered = 4 cycles × 2 meters/cycle = 8 meters
- Time taken = 4 cycles × 8 seconds/cycle = 32 seconds

4. **Calculating the Remaining Distance to the Pit**:
- After 4 cycles, the drunkard is at 8 meters.
- He needs to cover an additional distance of 3 meters to reach the pit at 11 meters.

5. **Moving Towards the Pit**:
- In the next cycle, the drunkard will take 5 steps forward:
- From 8 meters, he moves to 11 meters (5 steps forward).
- This takes him 5 seconds.

6. **Total Time Calculation**:
- Total time taken = Time for 4 cycles + Time for the last movement
- Total time = 32 seconds (for 4 cycles) + 5 seconds (to reach the pit) = 37 seconds

### Final Answer:
The drunkard will fall into the pit after **37 seconds**.

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