As Given ,
speed of A= 10m/s, B= 20m/s , C = 30m/s
length of track is 1000m
as we have find out , when all will meet first time ...so we have to calculate time taken by fastest runner over others ..
so C(30m/s fastest runner) take one round over B is = (1000 ) / (30+20)= 20 sec (as both are in opposite direction relative speed add)
similar C take one round over A is = (1000)/(30+10)= 25 sec.
now all will meet same first time = LCM(20,25) = 100sec ... so after 1min 40 sec , they all will meet first time