Train A travelling at 72 kmph crosses another train of half of its length travelling in opposite direction at speed of 90 kmph in 6 seconds. If train A crosses a platform in 29 seconds, then what is the length of the platform?

Options

A. A)400 meter
B. B)540 meter
C. C)480 meter
D. D)490 meter

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the Length of Train A
1. **Assume the length of Train A**: Let the length of Train A be \( L \).
2. **Length of Train B**: Since Train B is half the length of Train A, its length is \( \frac{L}{2} \).
3. **Relative Speed Calculation**: The relative speed of the two trains when they are moving towards each other is the sum of their speeds:
\[ \text{Speed of Train A} = 72 \text{ km/h} = \frac{72 \times 5}{18} = 20 \text{ m/s} \]
\[ \text{Speed of Train B} = 90 \text{ km/h} = \frac{90 \times 5}{18} = 25 \text{ m/s} \]
\[ \text{Relative Speed} = 20 + 25 = 45 \text{ m/s} \]
4. **Distance Covered in 6 seconds**: The total distance covered when both trains cross each other is:
\[ \text{Distance} = \text{Relative Speed} \times \text{Time} = 45 \text{ m/s} \times 6 \text{ s} = 270 \text{ m} \]
5. **Equation for Lengths**: The total distance is equal to the sum of the lengths of both trains:
\[ L + \frac{L}{2} = 270 \]
\[ \frac{3L}{2} = 270 \]
\[ 3L = 540 \implies L = 180 \text{ m} \]
Thus, the length of Train A is **180 meters**.

### Step 2: Calculate the Length of the Platform
1. **Total Distance when Train A crosses the platform**: The total distance covered when Train A crosses the platform is the length of Train A plus the length of the platform \( P \):
\[ \text{Total Distance} = L + P = 180 + P \]
2. **Speed of Train A in m/s**: We already calculated the speed of Train A as \( 20 \text{ m/s} \).
3. **Distance Covered in 29 seconds**: The distance covered by Train A while crossing the platform is:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 20 \text{ m/s} \times 29 \text{ s} = 580 \text{ m} \]
4. **Setting up the equation**: Now we can set up the equation:
\[ 180 + P = 580 \]
\[ P = 580 - 180 = 400 \text{ m} \]

### Conclusion
The length of the platform is **400 meters**.

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