2 guns were fired from same place at an interval of 28 mins. But a man sitting in the train approaching the place hears the 2nd firing 26 min after the 1st if the speed of sound is 325 m/sec, find the speed of train ?

Options

A. 25 km/hr
B. 25 m/sec
C. 75 km/hr
D. 50 m/sec

Answer

To solve the problem, we need to find the speed of the train based on the information provided about the firing of the guns and the time taken for the sound to reach the man in the train. Let's break down the solution step by step.

### Step-by-Step Solution

1. **Understanding the Time Difference**:
- The two guns were fired 28 minutes apart.
- The man in the train hears the second firing 26 minutes after the first firing.
- Therefore, the difference in time is \(28 \text{ minutes} - 26 \text{ minutes} = 2 \text{ minutes}\).

**Hint**: Calculate the difference between the time intervals to understand how much time the train saved.

2. **Convert Time to Seconds**:
- We need to convert the time difference from minutes to seconds for calculations.
- \(2 \text{ minutes} = 2 \times 60 = 120 \text{ seconds}\).

**Hint**: Remember to convert minutes to seconds by multiplying by 60.

3. **Calculate the Distance Sound Travels**:
- The speed of sound is given as \(325 \text{ m/s}\).
- The distance that sound travels in 120 seconds is calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 325 \text{ m/s} \times 120 \text{ s} = 39000 \text{ meters}. \]

**Hint**: Use the formula for distance (Distance = Speed × Time) to find how far the sound travels in the given time.

4. **Time Taken by the Train to Cover the Distance**:
- The train hears the second gunshot after 26 minutes, which we also need to convert to seconds:
- \(26 \text{ minutes} = 26 \times 60 = 1560 \text{ seconds}\).

**Hint**: Again, convert minutes to seconds for consistency in units.

5. **Calculate the Speed of the Train**:
- The speed of the train can be calculated using the formula:
\[ \text{Speed of Train} = \frac{\text{Distance}}{\text{Time}} = \frac{39000 \text{ meters}}{1560 \text{ seconds}}. \]
- Performing the division:
\[ \text{Speed of Train} = 25 \text{ m/s}. \]

**Hint**: Use the formula for speed (Speed = Distance / Time) to find the speed of the train.

6. **Convert Speed to km/h**:
- To convert the speed from meters per second to kilometers per hour, we use the conversion factor \(1 \text{ m/s} = 3.6 \text{ km/h}\):
- \(25 \text{ m/s} \times 3.6 = 90 \text{ km/h}\).

**Hint**: Remember the conversion factor to switch from m/s to km/h.

### Final Answer
The speed of the train is \(90 \text{ km/h}\).