A man travels at a speed of 20 Km/hr. and then returns at a speed of 30 Km/hr. His average speed of whole journey is

Options

A. 25 km/hr
B. 24.5 km/hr
C. 24 km/hr
D. 25.5 km/hr

Answer

To find the average speed of the whole journey when a man travels from point A to B at a speed of 20 km/hr and returns from B to A at a speed of 30 km/hr, we can follow these steps:

### Step 1: Define the Distance
Let the distance between point A and point B be \( x \) kilometers.

### Step 2: Calculate Time for Each Leg of the Journey
- **Time taken from A to B**:
\[ \text{Time}_{A \to B} = \frac{\text{Distance}}{\text{Speed}} = \frac{x}{20} \text{ hours} \]

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

### Step 3: Calculate Total Distance
The total distance for the whole journey (A to B and back to A) is:
\[ \text{Total Distance} = x + x = 2x \text{ kilometers} \]

### Step 4: Calculate Total Time
The total time for the whole journey is:
\[ \text{Total Time} = \text{Time}_{A \to B} + \text{Time}_{B \to A} = \frac{x}{20} + \frac{x}{30} \]

To add these fractions, find a common denominator (which is 60):
\[ \frac{x}{20} = \frac{3x}{60}, \quad \frac{x}{30} = \frac{2x}{60} \]
Thus,
\[ \text{Total Time} = \frac{3x}{60} + \frac{2x}{60} = \frac{5x}{60} = \frac{x}{12} \text{ hours} \]

### Step 5: Calculate Average Speed
The average speed for the whole journey is given by the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{2x}{\frac{x}{12}} = 2x \times \frac{12}{x} = 24 \text{ km/hr} \]

### Final Answer
The average speed of the whole journey is **24 km/hr**.

---