A train of length 150 m takes 10 s to cross another train 100 m long coming from opposite direction. If the speed of the first train is 30 km/hr, what is the speed of the second train?

Options

A. 72 km/hr
B. 60 km/hr
C. 54 km/hr
D. 48 km/hr

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Length of the first train (Train A) = 150 m
- Length of the second train (Train B) = 100 m
- Speed of Train A = 30 km/hr
- Time taken to cross each other = 10 seconds

2. **Convert the Speed of Train A to m/s:**
- Speed in m/s = Speed in km/hr × (5/18)
- Speed of Train A in m/s = 30 × (5/18) = 8.33 m/s

3. **Calculate the Total Distance Covered When Both Trains Cross Each Other:**
- Total distance = Length of Train A + Length of Train B
- Total distance = 150 m + 100 m = 250 m

4. **Use the Formula for Speed:**
- Speed = Distance / Time
- We know the total distance (250 m) and the time (10 s).
- Therefore, the relative speed of both trains when crossing each other = 250 m / 10 s = 25 m/s

5. **Set Up the Equation for Relative Speed:**
- The relative speed of the two trains when they are moving towards each other is the sum of their speeds.
- Let the speed of Train B be x km/hr. Convert this to m/s: x km/hr = x × (5/18) m/s.
- The equation for relative speed becomes:
\[ 8.33 + \left(\frac{5x}{18}\right) = 25 \]

6. **Solve for x:**
- Rearranging the equation:
\[ \frac{5x}{18} = 25 - 8.33 \]
\[ \frac{5x}{18} = 16.67 \]
- Multiply both sides by 18:
\[ 5x = 16.67 × 18 \]
\[ 5x = 300 \]
- Divide by 5:
\[ x = 60 \text{ km/hr} \]

7. **Conclusion:**
- The speed of the second train (Train B) is 60 km/hr.