Train A of length 240 m can cross a platform of length 480 m in 36 second. The ratio of speed of Train A and Train B is 4:5. Then find the length of Train B if Train B can cross a pole in 24 seconds .

Options

A. 560 m
B. 600 m
C. 640 m
D. 700 m

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the speed of Train A
- Given that Train A crosses a platform of length 480 m and its own length of 240 m in 36 seconds.
- The total distance covered by Train A while crossing the platform is:
\[ \text{Total Distance} = \text{Length of Train A} + \text{Length of Platform} = 240 \, \text{m} + 480 \, \text{m} = 720 \, \text{m} \]
- Using the formula for speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{720 \, \text{m}}{36 \, \text{s}} = 20 \, \text{m/s} \]

### Step 2: Determine the speed of Train B
- The ratio of the speeds of Train A and Train B is given as 4:5.
- Let the speed of Train A be \( 4k \) and the speed of Train B be \( 5k \).
- We have already calculated the speed of Train A as 20 m/s:
\[ 4k = 20 \implies k = 5 \]
- Therefore, the speed of Train B is:
\[ 5k = 5 \times 5 = 25 \, \text{m/s} \]

### Step 3: Calculate the length of Train B
- Train B crosses a pole in 24 seconds. When crossing a pole, the distance covered is equal to the length of the train.
- Using the formula for distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
- Thus, the length of Train B is:
\[ \text{Length of Train B} = \text{Speed of Train B} \times \text{Time} = 25 \, \text{m/s} \times 24 \, \text{s} = 600 \, \text{m} \]

### Final Answer
The length of Train B is **600 meters**.

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