Question:
A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is,
A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is,
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Add both train lengths to get the crossing distance, divide by the time to get relative speed, then subtract the known train's speed since they move toward each other.
Updated On: Jul 15, 2026
- 48 km/hr
- 54 km/hr
- 66 km/hr
- 82 km/hr
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The Correct Option is D
Solution and Explanation
Step 1: Add the lengths of both trains.
Train A is 108 m long and Train B is 112 m long. When two trains cross each other, together they must cover a distance equal to the sum of their lengths: \(108 + 112 = 220\) m.
Step 2: Find the relative speed from the crossing time.
They cross in 6 seconds, so relative speed = \(\frac{220 \text{ m}}{6 \text{ s}} = 36.67\) m/s.
Step 3: Convert relative speed to km/hr.
\(36.67 \text{ m/s} \times \frac{18}{5} = 132\) km/hr.
Step 4: Apply the opposite-direction rule.
When two objects move toward each other, their speeds add up to give the relative speed. So Speed of Train A + Speed of Train B = 132 km/hr.
Step 5: Solve for the second train's speed.
\(50 + \text{Speed of Train B} = 132\), so Speed of Train B = \(132 - 50 = 82\) km/hr. This matches option (4). Options (1), (2) and (3) would give a different relative speed that does not reproduce the 6-second crossing time when checked.
Train A is 108 m long and Train B is 112 m long. When two trains cross each other, together they must cover a distance equal to the sum of their lengths: \(108 + 112 = 220\) m.
Step 2: Find the relative speed from the crossing time.
They cross in 6 seconds, so relative speed = \(\frac{220 \text{ m}}{6 \text{ s}} = 36.67\) m/s.
Step 3: Convert relative speed to km/hr.
\(36.67 \text{ m/s} \times \frac{18}{5} = 132\) km/hr.
Step 4: Apply the opposite-direction rule.
When two objects move toward each other, their speeds add up to give the relative speed. So Speed of Train A + Speed of Train B = 132 km/hr.
Step 5: Solve for the second train's speed.
\(50 + \text{Speed of Train B} = 132\), so Speed of Train B = \(132 - 50 = 82\) km/hr. This matches option (4). Options (1), (2) and (3) would give a different relative speed that does not reproduce the 6-second crossing time when checked.
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