My Answer is 250

When two people are running in the same direction the relative speed is a difference in speeds of the two people.

In this case A=3 B=6 C=18

So relative speed of B wrt A is 6-3 = 3m/s
Relative speed of A wrt to C is 18-3 =15m/s

Therefore relative distances will be:
B wrt A is 750/3 =250
C wrt to A 750/15 = 50

LCM of 250 and 50 is 250 .

theres another method as well..

A takes 250seconds to colplete on round.( 750/3)

B takes 125

C takes 41.67

Hence A= 2B
B=3C

So after 250 lapse a would have completed 1 round B 2 and C 6.

hence 250

nikhilagrawal wrote:A, B and C run around a circular track of length 750m at speeds of 3 m/sec, 6 m/sec and 18 m/sec respectively. If all three start from the same point, simultaneously and run in the same direction, when will they meet for the first time after they start the race?

A. 750 seconds
B. 50 seconds
C. 250 seconds
D. 375 seconds
E. 75 seconds

Even I got 250 seconds.
Used the LCM method, its faster and better since you can always check your answer if its correct or not.