A man covers first half of its journey at 12 km/hr and the rest at 4 km/hr. His average speed is

Options

A. 3 km/hr
B. 6 km/hr.
C. 4.5 km/hr
D. 9 km/hr

Answer

To find the average speed of the man who covers the first half of his journey at 12 km/hr and the second half at 4 km/hr, we can use the formula for average speed when the distances are equal:

### Step-by-Step Solution:

1. **Identify the Speeds**:
- Let \( u = 12 \) km/hr (speed for the first half of the journey).
- Let \( v = 4 \) km/hr (speed for the second half of the journey).

2. **Use the Average Speed Formula**:
- The formula for average speed when the distances are equal is:
\[ \text{Average Speed} = \frac{2uv}{u + v} \]

3. **Substitute the Values into the Formula**:
- Substitute \( u \) and \( v \) into the formula:
\[ \text{Average Speed} = \frac{2 \times 12 \times 4}{12 + 4} \]

4. **Calculate the Denominator**:
- Calculate \( u + v \):
\[ 12 + 4 = 16 \]

5. **Calculate the Numerator**:
- Calculate \( 2 \times 12 \times 4 \):
\[ 2 \times 12 \times 4 = 96 \]

6. **Combine the Results**:
- Now substitute back into the average speed formula:
\[ \text{Average Speed} = \frac{96}{16} \]

7. **Perform the Division**:
- Calculate \( \frac{96}{16} \):
\[ \frac{96}{16} = 6 \text{ km/hr} \]

8. **Final Answer**:
- The average speed of the man is \( 6 \) km/hr.