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1. Two train 100 meters and 95 meters long respectively pass each other in 27 seconds, when they run in the same direction and in 9 seconds when they run in opposite directions. Speed of the two trains are?

A. 44 km/hr, 22 km/hr

B. 52 km/hr, 26 km/hr

C. 36 km/hr, 18 km/hr

D. 40 km/hr, 20 km/hr

Solution:

\begin{aligned} Let the speed of first train be \\ S_{1} km/hr and speed of second train \\ is S_{2} km/hr \\ As we know, \\ Time \\ = \frac{total distance}{relative speed in same/opposite direction} \\ In the same direction \\ \Rightarrow 27 sec  = \frac{(100 + 95)}{(S_{1} - S_{2}) \times \frac{5}{18}} \\ \Rightarrow 27 = \frac{195 \times 18}{(S_{1} - S_{2}) \times 5} \\ \Rightarrow S_{1} - S_{2} = 26....................... (i) \\ In the opposite direction, \\ \Rightarrow 9 = \frac{(100 + 95)}{(S_{1} + S_{2}) \times \frac{5}{18}} \\ \Rightarrow 9 = \frac{195 \times 18}{(S_{1} + S_{2}) \times 5} \\ \Rightarrow S_{1} + S_{2} = 39 \times 2 \\ \Rightarrow S_{1} + S_{2} = 78 \\ From equation (i) and (ii) \\ \Rightarrow S_{1} - S_{2} = 26 \\ \Rightarrow S_{1} + S_{2} = 78 \\ \Rightarrow S_{1} = \frac{26 + 78}{2} \\ \Rightarrow S_{1} = \frac{104}{2} \\ \Rightarrow S_{1} =  52 km/hr and \\ S_{2} =  26 km/hr \end{aligned}

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