Three friends, A, B, and C, are cycling on a circular track with a circumference of 3 km. They all start from the same point at 9:00 a.m. and travel in the same direction with speeds of 9 km/h, 12 km/h, and 15 km/h respectively. How many times will all three of them meet at the starting point if they continue cycling until 1:00 p.m.?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 3 i.e. 4 times.
Time taken by each to complete one round (in hours):
A = 3/9 = 1/3 hour = 20 minutes
B = 3/12 = 1/4 hour = 15 minutes
C = 3/15 = 1/5 hour = 12 minutes
LCM of 20, 15, 12 = 60
60 minutes = 1 hour
Total duration from 9 a.m. to 1 p.m. = 4 hours
Number of times they meet at the starting point = 4/1 = 4 times