Three men start together to travel the same way around a circular track of 11 km. Their speeds are 4, 5-5 and 8 kmph respectively. When will they meet at the starting point for the first time?

examrobotsa's picture
Q: 131 (IAS/2010)
Three men start together to travel the same way around a circular track of 11 km. Their speeds are 4, 5-5 and 8 kmph respectively. When will they meet at the starting point for the first time?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,7,4,0,3,7,1

keywords: 

{'circular track': [0, 0, 1, 1], 'speeds': [0, 0, 2, 2], 'hours': [7, 2, 16, 9], 'km': [0, 0, 2, 1], 'men': [4, 3, 12, 9]}

In this problem, the three men are traveling around a circular track at different speeds. To determine when they will all meet at the starting point again, we need to find the common multiple of their speeds. We also need to remember that they all started at the same point, so it`s their speeds, not the time it takes for them to complete a lap, that determines when they`ll meet again.

For option 1, 11 hours would not work as even the slowest person would have completed multiple rounds and none of the speeds are a factor of 11.

Option 2 suggests after 21 hours, but none of the runners` speeds multiplied by 21 gives an exact number of laps around an 11 km track.

Option 3 suggests 22 hours, which is correct because when each runner`s speed is multiplied by 22 and then divided by the track`s length (11 km), the result for each is an integer, indicating a complete number of laps and a meeting at the starting point.

Option 4 gives an answer of 33 hours, but similarly to option 2, when each speed is multiplied by 33 and then divided by the track length, it does not give a complete number of laps for all runners.