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1. A train, 300m long, passed a man, walking along the line in the same direction at the rate of 3 kmph in 33 seconds. The speed of the train is:

A. 30 kmph

B. 32 kmph

C. $32 \frac{8}{11}$ kmph

D. $35 \frac{8}{11}$ kmph

Solution:

Let the speed of train = x km/ hr
Length of train = 300 metres
Their relative speed in same direction
= (x - 3) km/hr
According to the question,

\frac{(300 + 0) m}{(x - 3) \times \frac{5}{18} m / s} = 33

[Here man's length is 0 metre]

\begin{aligned} \frac{100 \times 18}{5 x - 15} = 11 \\ 1800 = 55 x - 165 \\ 55 x = 1965 \end{aligned}

∴ Speed of the train =

\frac{1965}{55}

35 \frac{8}{11}

kmph

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