Two trains A and B, 100m and 60m long are moving in opposite directions on parallel tracks. The velocity of shorter train is 3 times that of the longer ones. If the trains take 4 seconds to cross each other the velocities of trains are

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$V_{A} = 5 {ms}^{- 1}; V_{B} = 15 {ms}^{- 1}$

$V_{A} = 5 {ms}^{- 1}; V_{A} = 15 {ms}^{- 1}$

$V_{A} = 20 {ms}^{- 1}; V_{B} = 60 {ms}^{- 1}$

$V_{A} = 10 {ms}^{- 1}; V_{B} = 30 {ms}^{- 1}$

answer is A.

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Detailed Solution

$\begin{array}{l} t = \frac{l_{A} + l_{B}}{V_{relative}} = \frac{l_{A} + l_{B}}{V_{A} + V_{B}} Let V_{A} = V, V_{B} = 3 V \\ t = \frac{100 + 60}{4 V} \end{array}$

$4 = \frac{160}{4 V} \Rightarrow V = 10$
V_A = 10m/s, V_B = 30m/s

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