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1. A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:

A. 45 m

B. 50 m

C. 54 m

D. 72 m

Solution:

\begin{aligned} 2 k m p h = (2 \times \frac{5}{18}) m/sec \\ = \frac{5}{9} m/sec \\ 4 k m p h = (4 \times \frac{5}{18}) m/sec \\ = \frac{10}{9} m/sec \\ Let the length of the train be x metres \\ and its speed be y m/sec \\ Then, \frac{x}{y - \frac{5}{9}} = 9 and \frac{x}{y - \frac{10}{9}} = 10 \\ ∴ 9 y - 5 = x and 10 (9 y - 10) = 9 x \\ \Rightarrow 9 y - x = 5 and 90 y - 9 x = 100 \\ On solving, we get : x = 50 \\ ∴ Length of the train is 50 m \end{aligned}

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