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 - Study24x7
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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

21s

B

29s

C

31s

D

37s

IIT Entrance Class 9 Class 12 (PCM)
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    • Each step taken by a drunkard requires a time of 1 second. If we see, after taking 5 steps forward, the drunkard takes 2 steps backward; therefore, the last 5 steps of the drunkard can be kept aside and we can calculate the rest of the distance to be covered and the time taken by the drunkard to cover that distance. We can then add both the times, for the initial journey and the last five steps, to get the final answer. Complete step by step answer: Given that, drunkard moves 5 steps forward and 3 steps backward in an interval of 8 seconds. After that, he is 2m away from the initial position. We get, x=5−3=2m in 8 seconds x=2m is the displacement of the drunkard in 8 seconds Velocity of the drunkard, v=Displacement Time We have, Displacement = 2mTime = 8s Therefore, v=28=14ms−1 Now, Time taken by drunkard to cover first 6m of his journey is given by, Time = DisplacementVelocity Distance to be covered, or displacement, is 6m And velocity is 14ms−1 Therefore, Time taken by drunkard to cover 6m distance is, t=614=6×4=24s The pit is 11m away from the initial position of drunkard. After covering 6m distance, the drunkard needs to take 5 more steps and he will fall into the pit. As given, each step takes 1 second to cover the distance; it means that after travelling 6m distance in 24 seconds, the drunkard will take 5 more seconds to fall into the pit. Total time taken by drunkard is, t=24+5=29s The drunkard will fall into the pit after 29s Hence, the correct option is A. Note: Students should not get confused between the distance covered by drunkard and the displacement of the drunkard. Furthermore, the speed of the drunkard should not be confused with his velocity. For falling into a pit, a drunkard needs to cover those 11 meters distance, which is drunkard’s displacement, and not the distance covered by him. Students have to work with velocity term instead of speed term for the drunkard, as velocity is associated with the total displacement, while speed is associated with the total distance covered by a body.

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    Reply 27 Jul 2021 12:55 PM
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