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. 30 km/h
B. 25 km/h
C. 40 km/h
D. 45 km/h

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Understand the scenario
We have two cars (Car A and Car B) moving in the same direction at a speed of 30 km/h, separated by a distance of 5 km. A third car (Car C) is moving in the opposite direction and meets both Car A and Car B at an interval of 4 minutes.

### Step 2: Convert the time from minutes to hours
Since the speed is given in km/h, we need to convert the time from minutes to hours for consistency.
- Time = 4 minutes = \( \frac{4}{60} \) hours = \( \frac{1}{15} \) hours.

### Step 3: Calculate the relative speed of Car C with respect to Cars A and B
Since Cars A and B are moving in the same direction at the same speed, their relative speed with respect to each other is 0. Therefore, we can focus on the relative speed of Car C with respect to the distance between Cars A and B.

The distance between Cars A and B is 5 km. The time taken for Car C to meet both cars is \( \frac{1}{15} \) hours.

Using the formula for speed:
\[ \text{Relative Speed of Car C} = \frac{\text{Distance}}{\text{Time}} = \frac{5 \text{ km}}{\frac{1}{15} \text{ hours}} = 5 \times 15 = 75 \text{ km/h} \]

### Step 4: Calculate the actual speed of Car C
The relative speed of Car C with respect to Cars A and B is 75 km/h. However, since Car C is moving in the opposite direction to Cars A and B, we need to subtract the speed of Cars A and B from the relative speed to find the actual speed of Car C.

\[ \text{Actual Speed of Car C} = \text{Relative Speed of Car C} - \text{Speed of Car A} = 75 \text{ km/h} - 30 \text{ km/h} = 45 \text{ km/h} \]

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

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