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1. Train A traveling at 63 kmph can cross a platform 199.5 m long in 21 seconds. How much would train A take to completely cross (from the moment they meet ) train B, 157 m long and traveling at 54 kmph in opposite direction which train A is traveling? (in seconds)

A. 16

B. 18

C. 12

D. 10

Solution:

\begin{aligned} Speed of train A \\ =  63 kmph \\ = (\frac{63 \times 5}{18}) m/sec \\ =  17 .5 m/sec \\ Speed of train B \\ =  54 kmph \\ = (\frac{54 \times 5}{18}) m/sec  =  15 m/sec \\ If the length of train A be x metre, \\ then \\ Speed of train A \\ = \frac{Length of train  +  length of platform}{Time taken in crossing} \\ \Rightarrow 17.5 = \frac{x + 199.5}{21} \\ \Rightarrow 17.5 \times 21 = x + 199.5 \\ \Rightarrow 367.5 = x + 199.5 \\ \Rightarrow x = 367.5 - 199.5 \\ \Rightarrow 168 metres \\ Relative speed \\ =  ( Speed train A +  Speed train B) \\ =  (17 .5 + 15)  m/sec \\ =  32 .5 m/sec \\ Required time \\ = \frac{Length of train A +   Length of train B}{Relative speed} \\ = (\frac{168 + 157}{32.5}) seconds \\ = 10 seconds \end{aligned}

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