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Speed, Time and Distance - Quant/Math - CAT 2010
Question 4 the day:
July 8, 2003
The question for the day is from the topic of Speed, Time and Distance.
- Three friends A, B and C run around a circular track of length 120 metres at speeds of 5 m/s, 7 m/sec and 15 m/sec, starting simultaneously from the same point and in the same direction. How often will the three of them meet?
| (1) |
Every 60 seconds |
| |
(2) |
Every 120 seconds |
| (3) |
Every 30 seconds |
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(4) |
None of these |
Correct Answer - (1)
Solution:
The problem can be solved as follows:
First find out when A and B will meet for the first time.
A and B will meet for the first time in (Circumference of track / relative speed) seconds = (120/2) = 60 seconds.
This also means that A and B will continue meeting each other every 60 seconds.
Next find out when B and C will meet for the first time.
B and C will meet for the first time in (120/8) = 15 seconds.
This also means that they will meet every 15 seconds after they meet for the first time.
i.e. A and B meet every 60 seconds and multiples of 60 seconds and B and C meet every 15 seconds and multiples of 15 seconds.
The common multiples to both these time, will be when A and B and B and C will meet – i.e when A, B and C will meet.
The common multiple of 60 and 15 will be 60, 120, 180 etc.
i.e. they will meet every 60 seconds.
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