A train 100 metres in length passes a milestone in 10 seconds and another train of the same length travelling in opposite direction in 8 seconds. The speed of the second train is -----

Options

A. 36 kmph
B. 48 kmph
C. 54 kmph
D. 60 kmph

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the speed of the first train
The first train passes a milestone in 10 seconds and is 100 meters long.

**Formula**:
Speed = Distance / Time

**Calculation**:
- Distance = 100 meters
- Time = 10 seconds

Speed of the first train = 100 meters / 10 seconds = 10 meters/second

### Step 2: Convert the speed of the first train to km/h
To convert meters/second to kilometers/hour, we use the conversion factor (1 m/s = 3.6 km/h).

**Calculation**:
Speed in km/h = 10 m/s × 3.6 = 36 km/h

### Step 3: Set up the equation for the second train
Let the speed of the second train be \( x \) km/h. Since the two trains are moving in opposite directions, the relative speed is the sum of their speeds.

**Equation**:
Relative speed = Speed of first train + Speed of second train
Relative speed = 36 km/h + \( x \) km/h

### Step 4: Calculate the time taken to cross each other
The second train is also 100 meters long and it crosses the first train in 8 seconds.

**Formula**:
Relative speed (in m/s) = Total distance / Time taken

**Total distance** when both trains cross each other = Length of first train + Length of second train = 100 meters + 100 meters = 200 meters.

**Calculation**:
Relative speed in m/s = 200 meters / 8 seconds = 25 m/s

### Step 5: Convert the relative speed to km/h
To convert the relative speed from meters/second to kilometers/hour:

**Calculation**:
Relative speed in km/h = 25 m/s × 3.6 = 90 km/h

### Step 6: Set up the equation for relative speed
Now, we can set up the equation using the relative speed we calculated:

**Equation**:
36 km/h + \( x \) km/h = 90 km/h

### Step 7: Solve for \( x \)
Now, we can solve for \( x \):

**Calculation**:
\( x = 90 - 36 \)
\( x = 54 \) km/h

### Conclusion
The speed of the second train is **54 km/h**.

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