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 16 kmph, 24 kmph and 32 kmph respectively. If the length of the track is 1600 metre, when will A, B and C meet at the starting point for the first time after they start the race?Solution
16km = 16000 m A makes it around the track 10 times (16000/1600) 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 is 12 IXAMBEE APPROACH: Time = Distance/Speed Time for A = 1.6/16 hours Time for B = 1.6/24 hours Time for C = 1.6/32 hours LCM of A,B,C = (LCM of numerator)/(HCF of Denominator) = (LCM of 1.6,1.6,1.6)/(HCF of 16,24,32) = 1.6/8 hours 1.6/8 hours = 12 minutes
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