A train of some length passes the platform of length 400 m in 45 seconds . Find the length of train if the speed of train is 66 km/hr .

Options

A. 476 m
B. None of these
C. 428 m
D. 410 m

Explanation

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

### Step 1: Convert the speed from km/hr to m/s
The speed of the train is given as 66 km/hr. We need to convert this speed into meters per second (m/s) using the conversion factor:
\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]
So,
\[ 66 \text{ km/hr} = 66 \times \frac{5}{18} \text{ m/s} \]
Calculating this gives:
\[ 66 \times \frac{5}{18} = 18.33 \text{ m/s} \]

### Step 2: Use the formula for distance
We know that distance is calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
In this case, the total distance covered by the train while passing the platform is equal to the length of the train (let's denote it as \( L \)) plus the length of the platform (400 m).

### Step 3: Calculate the total distance
The train passes the platform in 45 seconds. Therefore, the total distance covered by the train is:
\[ \text{Total Distance} = \text{Speed} \times \text{Time} \]
Substituting the values we have:
\[ \text{Total Distance} = 18.33 \text{ m/s} \times 45 \text{ s} \]
Calculating this gives:
\[ \text{Total Distance} = 825 \text{ m} \]

### Step 4: Set up the equation
The total distance covered by the train is equal to the length of the train plus the length of the platform:
\[ L + 400 = 825 \]

### Step 5: Solve for the length of the train
Now, we can solve for \( L \):
\[ L = 825 - 400 \]
Calculating this gives:
\[ L = 425 \text{ m} \]

### Conclusion
The length of the train is 425 meters.

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