Question : Train A running at 81 km/hr takes 72 sec to overtake train B, when both the trains are running in the same direction, but it takes 36 sec to cross each other if the trains are running in the opposite direction. If the length of train B is 600 metres, then find the length of train A (in metres).
Option 1: 600
Option 2: 480
Option 3: 590
Option 4: 900
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Correct Answer: 480
Solution :
Let the length of train A be $L{_A}$ and the speed of train B be $S{_B}$ km/hr.
When both trains are running in the same direction,
Distance = relative speed $\times$ time
⇒ $L{_A}+600 = (81-S{_B})\times\frac{5}{18}\times 72$
⇒ $L{_A}+600 = (81-S{_B})\times 20$
⇒ $L{_A}+20S{_B} = 1020$ ........(1)
When both the trains are running in the opposite direction,
⇒ $L{_A}+600 = (81+S{_B})\times\frac{5}{18}\times 36$
⇒ $L{_A}+600 = (81+S{_B})\times 10$
⇒ $L{_A}-10S{_B} = 210$
Multiplying by 2 we get,
⇒ $2L{_A} - 20S{_B} = 420$
⇒ $20S{_B} = 2L{_A} -420$........(2)
Now, putting the value from equation (2) in (1), we get,
⇒ $L{_A} + 20S{_B} = 1020$
⇒ $L{_A} + 2L{_A} - 420 = 1020$
⇒ $3L{_A} = 1440$
⇒ $L{_A} = 480\ \mathrm{m}$
Hence, the correct answer is 480.
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