Question
Aman and Bahadur are walking in the same direction beside a railroad track, and Aman is far behind Bahadur. Both walk at constant speeds, and Aman walks faster than Bahadur. A long train traveling at a constant speed in the same direction will take 10 seconds to pass Aman (from the front to the end) and will take 9 seconds to pass Bahadur. If it will take twenty minutes for the front of the train to travel from Aman to Bahadur, how many minutes will it take for Aman to catch up to Bahadur?
Answer: Option A
:
A
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A
Denote by VA,VB, and VT the speeds of Aman, Bahadhur, and the train,respectively .The relative speeds of the train with respect ti Aman and Bahadur are than VT−VA and VT−VB. It follows from the condition that the train passes Aman in 10 seconds and Bahadur in 9 seconds that
VT−VAVT−VB=910.
The relative speed of Aman with respect to Bahadur is VA−VB. We have
VA−VBVT−VB=VT−VBVT−VB−VT−VAVT−VB=1−910=110
Thus, Aman's speed with respect to Bahadur is ten times smaller than the train's, so, in order to reach Bahadur, it would take Aman ten times the time it would take the train, (i.e.,)200 minutes.
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