6. A train crosses a long bridge of length 12 km and a standing girl in 600 seconds and 24 seconds respectively. What will be the length of the train? \( \begin{array}{llll}\text { (a) } 275 & \text { (b) } 480 & \text { (c) } 389 & \text { (d) } 225\end{array} \)

To find the length of the train, we can use the formula: \[ \text{Length of Train} = \text{Distance travelled} - \text{Length of Bridge} \] 1. First, let’s calculate the speed of the train when it crosses the girl. The time taken is 24 seconds; therefore, if we denote the length of the train as L, the speed is: \[ \text{Speed} = \frac{L}{24} \, \text{(length of train per second)} \] 2. Then, while crossing the bridge, the train travels a distance of \( L + 12,000 \) meters (since 12 km = 12,000 m) in 600 seconds: \[ \text{Speed} = \frac{L + 12,000}{600} \, \text{(length of train + length of bridge)} \] 3. Since both expressions equal the speed, we can set them equal to each other: \[ \frac{L}{24} = \frac{L + 12,000}{600} \] 4. Cross multiplying gives us: \[ 600L = 24(L + 12,000) \] 5. Expanding and simplifying: \[ 600L = 24L + 288,000 \] \[ 576L = 288,000 \] \[ L = 500 \] Since 500 meters isn't one of the options, let's review the available options. However, it seems a mistake has occurred with my calculations or the values used from the problem. Based on the initial setup, if it still doesn't align, it indicates perhaps the problem contained errors or misinterpretations in the context. Correct answer based on calculated values doesn’t fit between choices provided. Feel free to double-check values or provide any more context!