Two trains A nad 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 after traveling for some time. After the meeting, train A takes 16 hours to reach its destination, and train B takes 9 hours to reach its destination.

### Step-by-Step Solution:

1. **Define Variables:**
- Let \( v_A = 120 \) km/h (speed of train A).
- Let \( v_B \) be the speed of train B (which we need to find).
- Let \( d_{PK} \) be the distance from point P to the meeting point K.
- Let \( d_{KQ} \) be the distance from the meeting point K to point Q.

2. **Distance Relationships:**
- After the meeting, train A travels to Q in 16 hours:
\[ d_{KQ} = v_A \times 16 = 120 \times 16 = 1920 \text{ km} \]
- After the meeting, train B travels to P in 9 hours:
\[ d_{PK} = v_B \times 9 \]

3. **Using the Time and Distance Relationship:**
- Since both trains meet at the same time, we can set up the following relationship based on the distances they cover before they meet:
\[ \frac{d_{PK}}{v_A} = \frac{d_{KQ}}{v_B} \]
- Substituting the distances we found:
\[ \frac{v_B \times 9}{120} = \frac{1920}{v_B} \]

4. **Cross-Multiply to Solve for \( v_B \):**
- Cross-multiplying gives:
\[ v_B^2 = 120 \times 1920 / 9 \]

5. **Calculate \( v_B^2 \):**
- First, calculate \( 120 \times 1920 \):
\[ 120 \times 1920 = 230400 \]
- Now divide by 9:
\[ v_B^2 = \frac{230400}{9} = 25600 \]

6. **Take the Square Root:**
- Now, take the square root to find \( v_B \):
\[ v_B = \sqrt{25600} = 160 \text{ km/h} \]

### Final Answer:
The speed of train B is **160 km/h**.