Three persons P, Q, R run along a circular track at speeds of 3 km/h, 4 km/h, 6 km/h, respectively. If the length of the track is 36 km, then after how much time will they meet again at the starting point?

36 hours

Time taken by P to cover the track = \(\frac{36}{3}\)

 = 12 hrs

 Time taken by Q to cover the track = \(\frac{36}{4}\)

 = 9 hrs

 Time taken by R to cover the track = \(\frac{36}{6}\)

 = 6 hrs

 LCM of 12, 9 and 6 = 36

Therefore, they all will meet again at the starting point after 36 hours.