Question

A drunkard walking in a narrow lane takes 8 steps forward and 6 steps backward, followed again by 8 steps forward and 6 steps backward and so on. Each step is 1 m long and requires 1 s. Determine how long the drunkard takes to fall in a pit 18 m away from the start

• A. 18 s
• B. 126 s
• C. 78 s
• D. 62 s

Answer 1

Answer: (C)

When the drunkard walks 8 steps forward and 6 steps backward, the displacement in the first 14 steps
$=8m-6m=2m$
Time taken for first 14 steps $=14s$
Time taken by drunkard to cover first 10 m of journey
$=\frac{14}{2}\times 10=70s$
If the drunkard takes 8 steps more, he will fall into the pit, so the time taken by the last 8 steps $=8s$
Total time taken $=70s+8s=78s$