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There are trains travelling on 4 parallel tracks

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There are trains travelling on 4 parallel tracks

by guerrero » Mon Jun 24, 2013 11:42 am
There are trains travelling on 4 parallel tracks. The frequencies of trains traveling on these tracks at equal interval of time are 4, 6, 8, 12 per hour respectively. If all trains start at 7 AM, after how much time will all the trains start together from the same place?

A. 1 Hour
B. 12 Hours
C. 24 Hours
D. 1/2 hours
E. 1/4 Hours

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by srcc25anu » Mon Jun 24, 2013 3:37 pm
First Approach:
Train A starts every 60/4 = 15 mins
Train B starts every 60/6 = 10 mins
Train C starts every 60/8 = 7.5 mins
Train D starts every 60/12 = 5 mins
LCM of above times = 30
Therefore after every 30 mins, all 4 trains start together.
Hence D

Second approch:
Train A starts every 60/4 = 15 mins
therefore train A starts at 7:00 - 7:15 - 7:30
Train B starts every 60/6 = 10 mins
therefore train B starts at 7:00 - 7:10 - 7:20 - 7:30
Train C starts every 60/8 = 7.5 mins
therefore train C starts at 7:00 - 7:07:30 sec - 7:15 - 7:22:30 secs : 7:30
Train D starts every 60/12 = 5 mins
therefore train D starts at 7:00 - 7:10 - 7:15 - 7:20 - 7:25 - 7:30
After 7:00, all 4 trains start together again at 7:30
Hence D
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