A train moving with a speed of 36 kmph takes 14 s to cross a bridge of length 100 m. The length of the train is

Options

A. 140 m
B. 40 m
C. 100 m
D. 360 m

Explanation

To find the length of the train, we can follow these steps:

### Step 1: Convert the speed of the train from km/h to m/s
The speed of the train is given as 36 km/h. To convert this to meters per second (m/s), we use the conversion factor:
\[ \text{Speed in m/s} = \text{Speed in km/h} \times \frac{5}{18} \]
Calculating this:
\[ \text{Speed} = 36 \times \frac{5}{18} = 10 \text{ m/s} \]

### Step 2: Calculate the total distance traveled by the train while crossing the bridge
The train takes 14 seconds to cross the bridge. We can find the total distance traveled by the train during this time using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Substituting the values we have:
\[ \text{Distance} = 10 \text{ m/s} \times 14 \text{ s} = 140 \text{ meters} \]

### Step 3: Relate the total distance to the length of the train and the bridge
When the train crosses the bridge, it travels a distance equal to the length of the bridge plus the length of the train. Let \( L \) be the length of the train. The total distance can be expressed as:
\[ \text{Total Distance} = \text{Length of the Bridge} + \text{Length of the Train} \]
Given that the length of the bridge is 100 meters, we can write:
\[ 140 \text{ meters} = 100 \text{ meters} + L \]

### Step 4: Solve for the length of the train
Rearranging the equation to find \( L \):
\[ L = 140 \text{ meters} - 100 \text{ meters} = 40 \text{ meters} \]

### Conclusion
The length of the train is 40 meters.

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