Question

A train clears a platform of 200 meters long in 10 seconds and passes a telegraph post in 5 seconds. The length of the train is :

• A. 100 meters
• B. 200 meters
• C. 300 meters
• D. 400 meters

Answer 1

Answer:

B. 200 meters

The length of the train is 200 meters.

Let $L$ be the length of the train (in meters) and $S$ be the speed of the train (in meters per second).

1. Scenario 1 (Passing the telegraph post):

   • When a train passes a tiny object like a post, the distance covered is equal to its own length.

   • Time = 5 seconds

   • Using $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$:

   • $S = \frac{L}{5}$
     (Equation 1)

2. Scenario 2 (Clearing the platform):

   • When a train passes a long structure like a platform, the total distance covered is its own length plus the length of the platform.

   • Total Distance = $L + 200$

   • Time = 10 seconds

   • Using $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$:
     $S = \frac{L + 200}{10}$
     (Equation 2)

3. Solve for $L$:
   Since the speed is constant, we can set the two equations equal to each other:
   $\frac{L}{5} = \frac{L + 200}{10}$

   Cross-multiply to solve:
   $10L = 5(L + 200)$

   $10L = 5L + 1000$
   $5L = 1000$
   $L = \frac{1000}{5} = \mathbf{200\text{ meters}}$