Two trains A and B start simultaneously in the opposite direction from two points P and Q and arrive at their destinations 16 and 9 hours respectively after their meeting each other at what speed does the second train B travel if the first train travels at 120 km/h per hour:

Options

A. 90 km/h
B. 160 km/h
C. 67.5 km/h
D. none of these

Answer

To solve the problem, we need to find the speed of train B given that train A travels at 120 km/h and they meet at a certain point. After they meet, train A takes 16 hours to reach its destination, while train B takes 9 hours.

### Step-by-Step Solution:

1. **Define the Variables:**
- Let the speed of train A be \( S_A = 120 \) km/h.
- Let the speed of train B be \( S_B \) km/h.
- Let the time taken by train A after meeting be \( T_A = 16 \) hours.
- Let the time taken by train B after meeting be \( T_B = 9 \) hours.

2. **Use the Relationship Between Speed, Time, and Distance:**
- The distance covered by train A after meeting can be expressed as:
\[ D_A = S_A \times T_A = 120 \times 16 = 1920 \text{ km} \]
- The distance covered by train B after meeting can be expressed as:
\[ D_B = S_B \times T_B = S_B \times 9 \]

3. **Set Up the Ratio of Distances:**
- Since both trains meet at the same point, the distances they cover after meeting are proportional to the times they take:
\[ \frac{D_A}{D_B} = \frac{T_B}{T_A} \]
- Plugging in the values:
\[ \frac{1920}{S_B \times 9} = \frac{9}{16} \]

4. **Cross-Multiply to Solve for \( S_B \):**
- Cross-multiplying gives:
\[ 1920 \times 16 = S_B \times 9 \times 9 \]
\[ 30720 = 81 S_B \]

5. **Solve for \( S_B \):**
- Dividing both sides by 81:
\[ S_B = \frac{30720}{81} \approx 379.26 \text{ km/h} \]

### Final Answer:
The speed of train B is approximately **379.26 km/h**.