Two cars are moving in the same direction with the same speed `30 km//hr`. They are separated by a distance of `5 km`, the speed of a car moving in the opposite direction of it meets these two cars at an interval of `4` minutes, will be.

Options

A. `40 km//hr`
B. `45 km//hr`
C. `10 km//hr`
D. `15 km//hr`

Explanation

To solve the problem, we need to find the speed of the car moving in the opposite direction (let's call it car C) that meets two cars (A and B) moving in the same direction at a speed of 30 km/h. The two cars are separated by a distance of 5 km, and car C meets them at an interval of 4 minutes.

### Step-by-Step Solution:

1. **Convert the time from minutes to hours**:
The time interval given is 4 minutes. To convert this into hours, we use the conversion factor:
\[ \text{Time in hours} = \frac{4 \text{ minutes}}{60} = \frac{1}{15} \text{ hours} \]

2. **Identify the speeds of cars A and B**:
Both cars A and B are moving at the same speed of 30 km/h.

3. **Calculate the relative speed of car C with respect to car A**:
Since car C is moving in the opposite direction, its speed will be negative when we consider the direction of cars A and B as positive. Thus, if the speed of car C is \( V_C \), the relative speed of car C with respect to car A is:
\[ V_{\text{relative}} = V_C + 30 \text{ km/h} \]

4. **Use the formula for distance**:
The distance between cars A and B is 5 km. The time taken for car C to meet car A is \( \frac{1}{15} \) hours. We can use the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Here, the distance is 5 km, and the speed is the relative speed we calculated in the previous step. Therefore, we have:
\[ 5 = (V_C + 30) \times \frac{1}{15} \]

5. **Rearranging the equation**:
To find \( V_C \), we rearrange the equation:
\[ 5 = \frac{V_C + 30}{15} \]
Multiplying both sides by 15 gives:
\[ 75 = V_C + 30 \]

6. **Solve for \( V_C \)**:
Now, subtract 30 from both sides:
\[ V_C = 75 - 30 = 45 \text{ km/h} \]

### Final Answer:
The speed of the car moving in the opposite direction (car C) is **45 km/h**.