Question

A train crossed a platform of 1200 m long in 15seconds and a bridge 3 km long in 35 seconds. Find the length of the train.

• A. 250m
• B. 150m
• C. 200m
• D. 190m
• E. None of these

Answer 1

The Correct Option is B

Step 1: Understand the problem.
The train crosses: - A platform of length 1200 meters in 15 seconds. - A bridge of length 3 kilometers (3000 meters) in 35 seconds.
Let the length of the train be \( L \) meters.

Step 2: Use the formula for speed.
The speed of the train can be calculated using the formula:
Speed = Distance / Time.
- When the train crosses the platform, the total distance covered is \( L + 1200 \) meters (since the train covers its own length and the length of the platform). - When the train crosses the bridge, the total distance covered is \( L + 3000 \) meters (since the train covers its own length and the length of the bridge).

The speed of the train can be calculated in both cases:
Speed = \( \frac{L + 1200}{15} \) (when crossing the platform)
Speed = \( \frac{L + 3000}{35} \) (when crossing the bridge)

Step 3: Set up the equation.
Since the speed is constant in both cases, we can equate the two expressions for speed:
\( \frac{L + 1200}{15} = \frac{L + 3000}{35} \)

Step 4: Solve for \( L \).
Cross-multiply to eliminate the fractions:
\( 35 \times (L + 1200) = 15 \times (L + 3000) \)
\( 35L + 42000 = 15L + 45000 \)
\( 35L - 15L = 45000 - 42000 \)
\( 20L = 3000 \)
\( L = \frac{3000}{20} \)
\( L = 150 \)

Step 5: Conclusion.
The length of the train is 150 meters.

Final Answer:
The correct option is (B): 150 meters.