Ans.
Distance covered by 1st train in 4 hours = 80*4 = 320 km
Relative speed of 2nd train = 120-80 = 40 km
It will overtake another train in 320/40 = 8 hours
Distance between overtake point and station A = 8*120 = 960 km
Speed of the train = 12000 / 10*60 = 20 m/s
Length of the train = Speed X time = 20 X 6 = 120m
Let length of platform be ?y?metres.
Then, at the platform,Distance travelled = y + (length of train) = (y + 480)m
Then, Speed of train = (y + 480)m / (3x60) sec = (y+480)/180 ...(1)
Also, at the pole,Distance travelled = length of train = 480m
Then, Speed of train = 480m / 30sec = 16 m/s ...(2)
Equating eq.(1) & eq.(2), we get,
(y+480)/180 = 16(y+480) = 16 x 180 = 2880
y = 2880 ?480 = 2400m or 2.4 km long platform.
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