Anjali and Babita are running on a circular track in opposite directions from same time at same point with speeds of 8 m/sec and 6 m/sec, respectively. If the length of the circular track is 960 m, how many times distinct points they will meet?

7 times

According to question ,

Time = \(\frac{DIstance}{SPeed}\)

Anjali  complete a round in =  \(\frac{960}{8}\) = 120 seconds

Babita  complete a round in = \(\frac{960}{6}\) = 160 seconds

They meet again at the starting point in , 

LCM(120,160) = 480 seconds

Now, relative speed of Anjali and Babita(when moves in opposite direction )  =

8 + 6 = 14 m/s

Time taken by them to cover 960 m = \(\frac{960}{14}\)) seconds

After every \(\frac{960}{14}\) seconds, they will meet on the track.

So in 480 seconds, the number of times they meet

=  \(\frac{480 × 14 }{960}\) = 7 times