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1. A train B speeding with 120 kmph crosses another train C running in the same direction, in 2 minutes. If the lengths of the trains B and C be 100m and 200m respectively, what is the speed (in kmph) of the train C?

A. 111 km

B. 123 km

C. 127 km

D. 129 km

Solution:

\begin{aligned} Relative speed of the trains \\ = (\frac{100 + 200}{2 \times 60}) m/sec \\ = (\frac{5}{2}) m/sec \\ Speed of train B \\ =  120 kmph \\ = (120 \times \frac{5}{18}) m/sec \\ = (\frac{100}{3}) m/sec \\ Let the speed of second train be x m/sec \\ Then, \frac{100}{3} - x = \frac{5}{2} \\ \Rightarrow x = (\frac{100}{3} - \frac{5}{2}) \\ = (\frac{185}{6}) m/sec \\ ∴ Speed of second train \\ = (\frac{185}{6} \times \frac{18}{5}) kmph \\ =  111 kmph \end{aligned}

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