The length of the bridge, which a train 400 metres long and travelling at 60 km/hr can crossin 36 seconds, is:

Options

A. 450 m
B. 250 m
C. 200 m
D. 500 m

Answer

To solve the problem of finding the length of the bridge that a train can cross, we can follow these steps:

### Step 1: Understand the Problem
We have a train that is 400 meters long and is traveling at a speed of 60 km/hr. The train crosses the bridge in 36 seconds. We need to find the length of the bridge.

### Step 2: Convert Speed from km/hr to m/s
To work with consistent units, we need to convert the speed from kilometers per hour (km/hr) to meters per second (m/s). The conversion factor is:
\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]
Thus,
\[ 60 \text{ km/hr} = 60 \times \frac{5}{18} = \frac{300}{18} = 16.67 \text{ m/s} \]

### Step 3: Calculate the Total Distance Covered
The total distance covered by the train while crossing the bridge is the sum of the length of the train and the length of the bridge. Let the length of the bridge be \( x \) meters. Therefore, the total distance is:
\[ \text{Total Distance} = \text{Length of Train} + \text{Length of Bridge} = 400 + x \text{ meters} \]

### Step 4: Use the Formula for Distance
We know that distance is equal to speed multiplied by time. The train crosses the bridge in 36 seconds, so:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Substituting the values we have:
\[ 400 + x = 16.67 \text{ m/s} \times 36 \text{ s} \]

### Step 5: Calculate the Right Side of the Equation
Now, calculate the right side:
\[ 16.67 \times 36 = 600 \text{ meters} \]
So we have:
\[ 400 + x = 600 \]

### Step 6: Solve for \( x \)
To find \( x \), we rearrange the equation:
\[ x = 600 - 400 \]
\[ x = 200 \text{ meters} \]

### Conclusion
The length of the bridge is 200 meters.

### Final Answer
The length of the bridge is **200 meters**.

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