Question

A circular field has a circumference of 480 km. Three cyclists Abhishek, Varun and Gautam start together and can cycle at speeds of 10 km/hr, 12 km/hr and 15 km/hr respectively, round the circular field. After how many hours will they meet again at the starting point

Answer 1

Hello Dear.

Circumference of the Circular Field = 480 km.

For Abhishek,
Speed of the Abhishek = 10 km/hr.
Time taken by the Abhishek to complete 1 round = 480/10
= 48 hr.

For Varun,
Speed of the Varun = 12 km/hr.
Time taken by the Varun to complete 1 round = 480/12
= 40 hr.

For Gautam,
Speed of the Gautam = 15 km/hr.
Time taken by the Gautam to complete 1 round = 480/15
= 32 hrs.


Now, Taking the L.C.M. of the time taken by the Abhishek, Gautam and Varun. 
L.C.M. of the 48, 40 and 32 hrs is 480 hrs.


Hence, after the time of 480 hrs all of the three, i.e. Abhishek, Varun, and Gautam will meet.


Hope it helps.

Answer 2

Time =Distance/speed

Time taken by Abhishek = 480/10 = 48 hours
Time taken by Varun = 480/12 = 40 hours
Time taken by Gautam = 480/15 = 32 hours

Time after which they'll meet = LCM of the time taken individually by the 3 people = 480 hours