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Three friends Ajay, Vijay and Sanjay move along a circular path of length 1.2 km with speeds of 6 km/h, 8 km/h and 9 km/h respectively. Ajay and Vijay move in the same direction but Sanjay move in opposite direction, if they all start at the same time and from same place. How many time will Ajay and Sanjay meets anywhere on the path by the time Ajay and Vijay for the first time anywhere on the path?
(a) 6 times
(b) 7 times
(c) 8 times
(d) 9 times
Three friends Ajay, Vijay and Sanjay move along a circular path of length 1.2 km with speeds of 6 km/h, 8 km/h and 9 km/h respectively. Ajay and Vijay move in the same direction but Sanjay move in opposite direction, if they all start at the same time and from same place. How many time will Ajay and Sanjay meets anywhere on the path by the time Ajay and Vijay for the first time anywhere on the path?
(a) 6 times
(b) 7 times
(c) 8 times
(d) 9 times
Answer is : (b) 7 times
Time taken by Ajay and Vijay to meet first time anywhere on the path
= Distance/Relative speed = 1.2/8.6 = 0.6 h
Time taken by Ajay and Sanjay to meet anywhere
= Distance/Relative speed \(=\frac{1.2}{9+6}\) = 0.8 h
The number of times Ajay and Sanjay meets anywhere on the path by the time Ajay and Vijay meets each other for the first time = 36/4.8 = 7 1/2, i.e. 7 times.