Two trains A and B start from Delhi and Patna towards Patna and Delhi, respectively. After passing each other, they take 16 h and 9 h to reach Patna and Delhi,respectively.If the train from Delhi is moving at 90 km/h, then find the speed of the other train (in km/h).

Options

A. a. 120
B. b. 190
C. c. 125
D. d. 145

Answer

To solve the problem step by step, we will use the information provided about the two trains and the time they take to reach their respective destinations after passing each other.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Speed of Train A (from Delhi) = 90 km/h
- Time taken by Train A to reach Patna after meeting = 16 hours
- Time taken by Train B (from Patna) to reach Delhi after meeting = 9 hours

2. **Use the Formula for Relative Speed:**
We can use the relationship between the speeds of the two trains and the times they take after they meet. The formula to find the speed of Train B (from Patna) is:
\[ \text{Speed of Train B} = \text{Speed of Train A} \times \sqrt{\frac{t_1}{t_2}} \]
where:
- \( t_1 \) = time taken by Train A after meeting = 16 hours
- \( t_2 \) = time taken by Train B after meeting = 9 hours

3. **Substitute the Values into the Formula:**
\[ \text{Speed of Train B} = 90 \times \sqrt{\frac{16}{9}} \]

4. **Calculate the Square Root:**
\[ \sqrt{\frac{16}{9}} = \frac{4}{3} \]

5. **Substitute Back into the Speed Formula:**
\[ \text{Speed of Train B} = 90 \times \frac{4}{3} \]

6. **Perform the Multiplication:**
\[ \text{Speed of Train B} = 90 \times \frac{4}{3} = 120 \text{ km/h} \]

7. **Final Answer:**
The speed of Train B is **120 km/h**.