A boat P is moving at 40 `"km"//"hr"` and another boat Q is moving at 20 `"km"//"hr"` Which one of the following is not a
possible value for their relative velocity-

Options

A. 10 `"km"//"hr"`
B. 20 `"km"//"hr"`
C. 30 `"km"//"hr"`
D. 40 `"km"//"hr"`

Explanation

To solve the problem of determining which value is not a possible relative velocity between two boats moving at different speeds, we can follow these steps:

### Step-by-step Solution:

1. **Identify the Speeds of the Boats**:
- Boat P is moving at a speed of 40 km/h.
- Boat Q is moving at a speed of 20 km/h.

2. **Understand Relative Velocity**:
- The relative velocity of one object with respect to another is given by the formula:
\[ V_{relative} = V_P - V_Q \]
- Here, \(V_P\) is the velocity of boat P, and \(V_Q\) is the velocity of boat Q.

3. **Calculate the Minimum Relative Velocity**:
- The minimum relative velocity occurs when the two boats are moving in opposite directions. Thus, the minimum value is:
\[ V_{relative, min} = V_P - V_Q = 40 \text{ km/h} - 20 \text{ km/h} = 20 \text{ km/h} \]

4. **Calculate the Maximum Relative Velocity**:
- The maximum relative velocity occurs when the two boats are moving in the same direction. Thus, the maximum value is:
\[ V_{relative, max} = V_P + V_Q = 40 \text{ km/h} + 20 \text{ km/h} = 60 \text{ km/h} \]

5. **Determine the Range of Possible Relative Velocities**:
- Therefore, the possible values for the relative velocity of the two boats lie between the minimum and maximum values:
\[ 20 \text{ km/h} \leq V_{relative} \leq 60 \text{ km/h} \]

6. **Identify Values Outside the Range**:
- Any value below 20 km/h or above 60 km/h is not a possible relative velocity.

7. **Conclusion**:
- If the options provided include values such as 10 km/h, 20 km/h, 30 km/h, and 40 km/h, the value that is not possible is 10 km/h, as it is below the minimum relative velocity of 20 km/h.

### Final Answer:
The value that is not a possible relative velocity is **10 km/h**.