Question : Two trains 150 m and 120 m long respectively moving from opposite directions cross each other in 10 seconds. If the speed of the second train is 43.2 km/hr, then the speed of the first train is:
Option 1: 54 km/hr
Option 2: 50 km/hr
Option 3: 52 km/hr
Option 4: 51 km/hr
Correct Answer: 54 km/hr
Solution :
Let the speed of the first train be $x$ km/hr.
Then, the relative speed of the two trains in opposite directions is $(43.2 + x)$ km/hr.
The total distance covered by the two trains in 10 seconds = 150 + 120 = 270 m
Distance = Speed × Time
$⇒270 = (43.2 + x) \times \frac{5}{18} \times 10$
$⇒270\times \frac{18}{10} = (43.2 + x) \times 5$
$⇒486=216+5x$
$\therefore x = \frac{486 - 216}{5} = 54$
Hence, the correct answer is 54 km/hr.
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