Question
'Arjuna' and 'Bishnu' began
running in opposite directions on a circular track of 1200 metres at the same time. If 'Arjuna', who is twice as fast as 'Bishnu', is running clockwise, what is the shortest distance between their starting point and the point where they first meet?Solution
ATQ, Let speed of 'Arjun' and 'Bishu' be '2a' m/s and 'a' m/s, respectively And, let they meet after 't' seconds. So, 2a × t + a × t = 1200 Or, t = (1200/3x) = (400/a) Required distance = distance travelled by 'Bishnu' in 't' seconds = (400/a) × a = 400 metres Alternate solution Ratio of speeds of 'Arjuna' and 'Bishnu' = 2:1 Since, time is constant. So, ratio of distance travelled by 'Arjuna' and 'Bishnu' = 2:1 So, required distance = 1200 × (1/3) = 400 metres
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