A drunkard is walking along a straight 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. 21 s
B. 29 s
C. 31 s
D. 37 s

Explanation

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

### Step-by-Step Solution:

1. **Understand the Drunkard's Movement:**
The drunkard takes 5 steps forward and then 3 steps backward. Each step is 1 meter long and takes 1 second.

2. **Calculate the Net Movement in One Cycle:**
- In one complete cycle (5 steps forward and 3 steps backward):
- Forward distance = 5 m
- Backward distance = 3 m
- Net distance covered in one cycle = Forward distance - Backward distance = 5 m - 3 m = 2 m.

3. **Determine the Time Taken for One Cycle:**
- Total steps in one cycle = 5 (forward) + 3 (backward) = 8 steps.
- Since each step takes 1 second, the total time for one cycle = 8 seconds.

4. **Calculate the Number of Cycles to Reach the Pit:**
- The pit is located 11 m away from the starting point.
- After each cycle, the drunkard moves 2 m forward.
- To find the number of complete cycles needed to reach or exceed 11 m:
- Distance after n cycles = 2n.
- We need to find n such that 2n ≥ 11.
- Solving for n: n = 11/2 = 5.5 cycles.
- Since the drunkard cannot complete half a cycle, he will complete 5 cycles.

5. **Calculate the Distance After 5 Cycles:**
- After 5 cycles, the distance covered = 2 * 5 = 10 m.
- Time taken for 5 cycles = 8 seconds/cycle * 5 cycles = 40 seconds.

6. **Determine the Remaining Distance to the Pit:**
- After 5 cycles, the drunkard is at 10 m. The pit is at 11 m, so he has 1 m left to walk.

7. **Final Step to the Pit:**
- In the next cycle, he will take 5 steps forward (1 m each), reaching 15 m, and then take 3 steps backward (1 m each), ending up at 12 m.
- However, since he only needs to walk 1 more meter to reach the pit, he will fall into the pit after taking 1 more step forward.

8. **Calculate the Total Time Until He Falls:**
- He has already taken 40 seconds for the first 5 cycles.
- He will take 1 more second to take that final step forward into the pit.
- Total time = 40 seconds + 1 second = 41 seconds.

### Conclusion:
The drunkard will fall into the pit after **41 seconds**.