Two trains of length 110 m and 90 m are running on parallel lines in the same direction with a speed of 45 km/h and 50km/h respectively . In what time will they pass other ?

Options

A. 136 s
B. 138 s
C. 142 s
D. None of these

Explanation

To solve the problem of how long it will take for the two trains to pass each other, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Lengths of the Trains:**
- Length of Train 1 = 110 m
- Length of Train 2 = 90 m

2. **Identify the Speeds of the Trains:**
- Speed of Train 1 = 45 km/h
- Speed of Train 2 = 50 km/h

3. **Calculate the Relative Speed:**
Since the trains are moving in the same direction, we subtract the speed of Train 1 from the speed of Train 2 to find the relative speed.
\[ \text{Relative Speed} = \text{Speed of Train 2} - \text{Speed of Train 1} = 50 \text{ km/h} - 45 \text{ km/h} = 5 \text{ km/h} \]

4. **Convert the Relative Speed to meters per second:**
To convert km/h to m/s, we use the conversion factor \( \frac{5}{18} \).
\[ \text{Relative Speed in m/s} = 5 \text{ km/h} \times \frac{5}{18} = \frac{25}{18} \text{ m/s} \]

5. **Calculate the Total Length of the Trains:**
The total length that needs to be covered for the trains to completely pass each other is the sum of their lengths.
\[ \text{Total Length} = 110 \text{ m} + 90 \text{ m} = 200 \text{ m} \]

6. **Use the Formula for Time:**
The time taken to pass each other can be calculated using the formula:
\[ \text{Time} = \frac{\text{Total Length}}{\text{Relative Speed}} \]
Substituting the values we have:
\[ \text{Time} = \frac{200 \text{ m}}{\frac{25}{18} \text{ m/s}} = 200 \times \frac{18}{25} \]

7. **Calculate the Time:**
\[ \text{Time} = \frac{200 \times 18}{25} = \frac{3600}{25} = 144 \text{ seconds} \]

### Final Answer:
The time taken for the two trains to pass each other is **144 seconds**.