Question

A train passes a standing man in 6 seconds and 210 m long platform in 16 seconds. The length and speed of the train, respectively, is:

• A. 126 m, 21 m/s
• B. 120 m, 20 m/s
• C. 110 m, 20 m/s
• D. 63 m, 21 m/s

Hint:

When a train passes a platform, the total distance covered is the sum of the length of the train and the length of the platform. Use this to set up equations to solve for the length and speed of the train.

Answer 1

The Correct Option is A

Step 1: Understanding the relationship.
Let the length of the train be \( L \) meters and the speed of the train be \( v \) meters per second. When the train passes a standing man, it covers its own length, \( L \), in 6 seconds. Hence, the speed of the train can be calculated as: \[ v = \frac{L}{6} \] When the train passes a platform of length 210 m, it covers a distance equal to the length of the train plus the length of the platform, i.e., \( L + 210 \) meters, in 16 seconds. So, the speed of the train can also be written as: \[ v = \frac{L + 210}{16} \] Step 2: Set up the equations.
From the two equations for speed \( v \), we have: \[ \frac{L}{6} = \frac{L + 210}{16} \] Step 3: Solve for \( L \).
Cross-multiply to solve for \( L \): \[ 16L = 6(L + 210) \] Expanding the equation: \[ 16L = 6L + 1260 \] Simplifying: \[ 16L - 6L = 1260 \quad \Rightarrow \quad 10L = 1260 \quad \Rightarrow \quad L = \frac{1260}{10} = 126 \, {m} \] Step 4: Calculate the speed of the train.
Now, substitute \( L = 126 \) into the equation \( v = \frac{L}{6} \) to find the speed: \[ v = \frac{126}{6} = 21 \, {m/s} \] Step 5: Conclusion.
The length of the train is 126 meters and the speed is 21 m/s. Thus, the correct answer is (1) 126 m, 21 m/s.