A car travels from A to B at a speed of `20 km//hr` and returns at a speed of `30 km//hr`. The average speed of the car for the whole journey is

Options

A. `25 km//hr`
B. `24 km//hr`
C. `50 km//hr`
D. `5 km//hr`

Answer

To find the average speed of the car for the entire journey from A to B and back to A, we can follow these steps:

### Step 1: Define the distances and speeds
Let the distance from A to B be \( x \) km. The speed from A to B is \( 20 \) km/hr and the speed from B to A is \( 30 \) km/hr.

### Step 2: Calculate the time taken for each leg of the journey
- **Time taken to travel from A to B**:
\[ T_1 = \frac{x}{20} \text{ hours} \]

- **Time taken to travel from B to A**:
\[ T_2 = \frac{x}{30} \text{ hours} \]

### Step 3: Calculate the total time taken for the journey
The total time taken \( T \) is the sum of the time taken for each leg:
\[ T = T_1 + T_2 = \frac{x}{20} + \frac{x}{30} \]

To add these fractions, we need a common denominator. The least common multiple of \( 20 \) and \( 30 \) is \( 60 \):
\[ T = \frac{3x}{60} + \frac{2x}{60} = \frac{5x}{60} = \frac{x}{12} \text{ hours} \]

### Step 4: Calculate the total distance covered
The total distance covered during the journey is:
\[ \text{Total distance} = x + x = 2x \text{ km} \]

### Step 5: Calculate the average speed
The average speed \( V_{avg} \) is given by the formula:
\[ V_{avg} = \frac{\text{Total distance}}{\text{Total time}} = \frac{2x}{\frac{x}{12}} \]

Simplifying this expression:
\[ V_{avg} = 2x \times \frac{12}{x} = 24 \text{ km/hr} \]

### Final Answer
The average speed of the car for the whole journey is \( 24 \) km/hr.

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