Two trains travelling in the same direction at 40 km/hr. and 22 km/hr completely pass one another in 1 minute. If the length of the first train is 125 metres, the length of the second train is:

Options

A. 125 metres
B. 150 metres
C. 175 metres
D. 200 metres

Answer

To solve the problem of finding the length of the second train, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the speeds of the trains**:
- Speed of the first train (Train A) = 40 km/hr
- Speed of the second train (Train B) = 22 km/hr

2. **Convert the speeds from km/hr to m/s**:
- To convert km/hr to m/s, we use the formula:
\[ \text{Speed in m/s} = \text{Speed in km/hr} \times \frac{5}{18} \]
- For Train A:
\[ 40 \times \frac{5}{18} = \frac{200}{18} \approx 11.11 \text{ m/s} \]
- For Train B:
\[ 22 \times \frac{5}{18} = \frac{110}{18} \approx 6.11 \text{ m/s} \]

3. **Calculate the relative speed of the two trains**:
- Since the trains are moving in the same direction, the relative speed is the difference of their speeds:
\[ \text{Relative Speed} = 40 - 22 = 18 \text{ km/hr} \]
- Convert this to m/s:
\[ 18 \times \frac{5}{18} = 5 \text{ m/s} \]

4. **Determine the total distance covered when the trains pass each other**:
- Let the length of the second train be \( x \) meters.
- The total distance when both trains pass each other is the sum of their lengths:
\[ \text{Total Distance} = 125 + x \text{ meters} \]

5. **Use the time taken to pass each other**:
- The problem states that they completely pass each other in 1 minute (60 seconds).
- Using the formula \( \text{Distance} = \text{Speed} \times \text{Time} \):
\[ 125 + x = \text{Relative Speed} \times \text{Time} \]
\[ 125 + x = 5 \times 60 \]
\[ 125 + x = 300 \]

6. **Solve for \( x \)**:
- Rearranging the equation gives:
\[ x = 300 - 125 \]
\[ x = 175 \text{ meters} \]

### Final Answer:
The length of the second train is **175 meters**.