A train of some length passes the platform of length 524 metres in 55 seconds. Find the length of train if the speed of train is 72 km/hr.

Options

A. 476 metres
B. None of these
C. 428 metres
D. 576 metres

Answer

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

### Step 1: Convert the speed of the train from km/hr to m/s
The speed of the train is given as 72 km/hr. To convert this to meters per second, we use the conversion factor:
\[ \text{Speed in m/s} = \text{Speed in km/hr} \times \frac{5}{18} \]

Calculating:
\[ \text{Speed} = 72 \times \frac{5}{18} = 20 \text{ m/s} \]

### Step 2: Use the formula for speed
The formula for speed is given by:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

In this case, the distance is the length of the train plus the length of the platform. We know the length of the platform is 524 meters and the time taken to pass the platform is 55 seconds.

### Step 3: Set up the equation
From the speed formula, we can express the distance as:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Substituting the known values:
\[ \text{Distance} = 20 \text{ m/s} \times 55 \text{ s} = 1100 \text{ meters} \]

### Step 4: Relate the distance to the lengths
The total distance covered when the train passes the platform is the sum of the length of the train (L) and the length of the platform (524 m):
\[ L + 524 = 1100 \]

### Step 5: Solve for the length of the train
Now, we can solve for L:
\[ L = 1100 - 524 \]
\[ L = 576 \text{ meters} \]

### Conclusion
The length of the train is 576 meters.

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