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1. A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:

A. 50 m

B. 150 m

C. 200 m

D. Data inadequate

Solution:

\begin{aligned} Let the length of the train be x metres \\ and its speed by y m/sec \\ T h e n, \frac{x}{y} = 15 \Rightarrow y = \frac{x}{15} \\ ∴ \frac{x + 100}{25} = \frac{x}{15} \\ \Rightarrow 15 (x + 100) = 25 x \\ \Rightarrow 15 x + 1500 = 25 x \\ \Rightarrow 1500 = 10 x \\ \Rightarrow x = 150 m \end{aligned}

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