A,B AND C START CYCLING AROUND A CIRCULAR PATH IN THE SAME DIRECTION AT SAME TIME. CIRCUMFERENCE OF THE PATH IS 1980M. IF THE SPEED OF A IS 330M/MIN , SPEED OF B IS 198M/MIN AND C IS 220M/MIN AND THEY START FROM THE SAME POINT THEN AFTER WHAT TIME INTERVAL THEY WILL BE TOGETHER AT THE STARTING POINT.

A will complete one round in 1980/330 = 6 min 

B will complete one round in 1980/198 = 10 min 

C will complete one round in 1980/220 = 9 min 

 

Now, let A, B and C meet after time t and they would have respectively completed, n1, n2 and n3 rounds and they would be be x distance away from the start point

 

Hence, 330t = x + 1980n1

198t = x + 1980n2

220t = x + 1980n3

 

Substituting x from equation 1 into 2 and 3

198t = 330t - 1980n1 + 1980n2

1980(n1-n2) = 132t

t = 15(n1-n2)

 

Also,  220t = 330t - 1980n1 + 1980n3

1980(n1-n3) = 110t

Since t is same, and n1-n3 and n1-n2 can be any whole number, so we need to compute LCM of 15 and 18 which is 90

Hence, A,B and C will meet after 90 min.