Question

A drunkard is walking along a straight road. He takes $5$ steps forward and $3$ 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:
(A) $21\,s$
(B) $29\,s$
(C) $31\,s$
(D) $37\,s$

Answer 1

Distance covered by the drunkard is calculated by adding the forward step and subtracting the backward step. By doing this, the time taken to reach the pit which is at some distance from the starting point of the drunkard is calculated.

Formulae Used:
Distance covered by the walking of the drunkard is given by
Distance covered = $f - b$
Where, $f$ is the forward step and $b$ is the backward step.

Complete step-by-step solution:
The given data from the question are
Number of forward steps taken by drunkard, $f = 5$
Number of forward steps taken by drunkard, $b = 3$
Length of one step, $s = 1\,m$
Time taken to travel one step, $t = 1\,s$
Distance of pit from the starting point, $D = 11\,m$
Distance covered is directly proportional to the time taken. At first the drunkard takes the forward step of 5.
Hence the distance covered is $d = 5\,m$ , since distance covered by single step is 1 m.Next he takes three backward steps,
Distance moved forward = $5\,m - 3\,m$
Distance moved forward = $2\,m$
Hence to cover $2\,m$, $8\,s$walking is required. Similarly, the distance and time taken increases linearly.
For a distance of $4\,m$, time taken is $16\,s$
For a distance of $8\,m$, time taken is $32\,s$
The pit is at the distance of $11\,m$from the starting point, hence for the next $5\,m$ drunkard walks forward to reach the pit. So, time taken is $32\,s + 5\,s = 37\,s$.
Thus, the option (D) is correct. The drunkard takes $37\,s$ to reach the pit.

Note:- Care must be taken in calculating the total distance covered forward. This is because the backward step must be subtracted from the forward step to calculate the distance travelled by the drunkard. Adding the forward step and subtracting the backward step continuous until the distance reaches the pit.