A train 140 metre long is running at 60 km/hour. How much time will it take to pass a platform 260 metre long?

Question

Accepted Answer

To determine how much time the train will take to pass the platform, we need to calculate the total distance the train needs to cover and the speed at which it is traveling.

1. **Total Distance to Cover:**
   - The train is 140 meters long, and it needs to pass a platform that is 260 meters long.
   - Therefore, the total distance to cover is the length of the train plus the length of the platform: 
     $$
     140 \, \text{meters} + 260 \, \text{meters} = 400 \, \text{meters}
     $$

2. **Speed of the Train:**
   - The train is running at a speed of 60 km/hour.
   - To use this speed in our calculation, we need to convert it to meters per second:
     $$
     60 \, \text{km/hour} = \frac{60 \times 1000}{3600} \, \text{meters/second} = \frac{60000}{3600} \, \text{meters/second} = 16.67 \, \text{meters/second}
     $$

3. **Time Calculation:**
   - Time is calculated by dividing the total distance by the speed:
     $$
     \text{Time} = \frac{\text{Total Distance}}{\text{Speed}} = \frac{400 \, \text{meters}}{16.67 \, \text{meters/second}} \approx 24 \, \text{seconds}
     $$

Therefore, the train will take approximately 24 seconds to pass the platform, which corresponds to Option 2.

**Explanation of Incorrect Options:**

- **Option 1 (18 sec):** This option is incorrect because the calculated time of 24 seconds is significantly greater than 18 seconds. The train cannot cover the total distance of 400 meters in just 18 seconds at the given speed.

- **Option 3 (30 sec):** This option is incorrect because the calculated time of 24 seconds is less than 30 seconds. The train will pass the platform faster than 30 seconds.

- **Option 4 (32 sec):** This option is incorrect because the calculated time of 24 seconds is less than 32 seconds. The train will complete passing the platform in a shorter time than 32 seconds.

In conclusion, the correct answer is Option 2, which is 24 seconds, as it accurately reflects the time required for the train to pass the platform based on the given speed and distances.