Q. 13: Anil, Sunil, and Ravi run along a circular path of length 3 km, starting from the same point at the same time, and going in the clockwise direction. If they run at speeds of 15 km/hr, 10 km/hr, and 8 km/hr, respectively, how much distance in km will Ravi have run when Anil and Sunil meet again for the first time at the starting point?
We are given the individual speeds of Anil, Sunil and Ravi, which are 15 kmph, 10 kmph and 8 kmph respectively.
We are also told that the length of the track is 3 KM.
Let us calculate the time taken by Anil and Sunil to complete one round(which is 3KM in length):
Time taken by Anil to complete one round in minutes
Time taken by Sunil to complete one round in minutes
Anil completing each round in 12 minutes, reaches the starting point at 12, 24, 36, 48, 60 …. minutes
Sunil completing each round in 18 minutes, reaches the starting point at 18, 36, 54, 72, 90 …. minutes
Clearly, both of them reach the starting point at 36 minutes, for the first time together.
Observe that 36 is teh LCM of 12 and 18
The distance covered by Ravi, whose speed is 8 kmph in 36 minutes(or 36/60 = 0.6 hours) = 8 × 0.6 = 4.8 km