Happy and Sad are running on a circular track of radius 245 metres. Happy can complete a round in 200 seconds and the speed of Sad is twice the speed of Happy. They started simultaneously towards each other from two points diametrically opposite on the circular path. If they first meet at a point they called it a danger point which is between the two points A and B from where they have started their race, After how much time from the start do they met at danger point for the third time?
Length of the track = 2 × 22/7 × 245 = 1540 metre Distance to be covered for the first meeting = 1540/2 = 770metre Speed of Happy = 1540/200 = 7.7 m/s Speed of Sad = 1540/100 = 15.4 m/s Time taken from the start of first meeting = 770/((7.7+15.4))= 770/23.1 = 331/3 seconds Time taken for Happy and Sad to meet again at Danger Point = LCM of time taken by them to go around the track once = LCM of 1540/7.7 and 1540/15.4 = LCM of 200 and 100 = 200 seconds So, the total required time = 100/3 + 200 +200 = 1300/3 seconds = `433(1/3)` seconds