A train daily overtakes a cyclist at a fixed time and fixed place. One day cyclist is late by 25 minutes and hence train overtakes him at a point 6 km earlier than the fixed place. Find the speed of the train, if the speed of the cyclist is 12 km/hr.
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Let the train daily overtakes the cyclist at a fixed point A and a fixed time.
One day cyclist late by 25 minutes, So, cyclist will rach at fixed point by 25 minutes late.
But train overtakes cyclist 6 km before the fixed point.
The time taken by cyclist to reach at fixed point after crossing the train,
= 6/12 = 1/2 hours = 30 min.
Thus, Difference between time taken by cyclist usual and on late day at Point B , 6 km before the fixed point = 30 - 25 = 5 min.
So, Train will take 5 minutes to reach at fixed point from B.
So, Ratio of speed = 6:1.
Speed of the train = 72 kmph.