A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at

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Q: 49 (IAS/2003)
‘A’ walks around a circular field at the rate of one round per hour while ‘B’ runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,3,6,2,1,3,3

keywords: 

{'circular field': [0, 0, 1, 0], 'hour': [5, 5, 11, 12], 'rounds': [1, 0, 1, 0], 'round': [0, 0, 1, 1], 'rate': [2, 3, 13, 20], 'same direction': [0, 0, 2, 2]}

The question is about time, speed, and distance on a circular track. `A` walks one round per hour and `B` runs six rounds per hour, which means `B` is five times faster than `A`. They start together, so they will meet when `B` completes one more round than `A`. If `A` completes one round in an hour, `B` completes this in 1/5th of an hour which is 12 minutes (60/5).

Option 1 and 2 are both over an hour after they start, this wouldn`t be the first time they cross. `B` should be catching up to `A` before an hour. Option 3, 7:48 a.m., is 18 minutes past start time, while option 4, 7:42 a.m., is 12 minutes past 7:30 a.m. which matches with the calculation above. Therefore, option 4 is correct. They will cross each other first at 7:42 a.m.

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