Question
A,B and C run around a Circular track starting from the
same point simultaneously and in the same direction at the speed of 8 kmph, 12 kmph and 16 kmph respectively. If the length of the track is 800 metre, when will A, B and C meet at the starting point for the first time after they start the race?Solution
8km = 8000 m A makes it around the track 10 times (8000/800) in an hour Similarly B = 15 times and C = 20 times in an hour In 60 minutes, A will complete track once every 6 minutes, B once every 4 minutes and C once every 3 minutes LCM of A,B,C = LCM(6,4 & 3)= 12Ā Alternative:Ā Time = Distance/Speed Time for A = 0.8/8 hours Time for B = 0.8/12 hours Time for C = 0.8/16 hours LCM of A,B,C = (LCM of numerator)/(HCF of Denominator) = (LCM of 0.8,0.8,0.8)/(HCF of 8,12,16) = 0.8/4 hours 0.8/4 hours = 12 minutes
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