Shektan walked a distance at a speed of 8 km/h. He was in a hurry so on the return journey he travelled in an autorickshaw at a speed of 24 Km/h. Find his average speed for the entire journey .

Options

A. 20 km/h
B. 32 km/h
C. 12 km/h
D. 16 km/h

Answer

To find the average speed for the entire journey, we can use the formula for average speed when the distances are the same for both parts of the journey. The average speed can be calculated using the formula:

\[ \text{Average Speed} = \frac{2 \times v_1 \times v_2}{v_1 + v_2} \]

where \( v_1 \) is the speed for the first part of the journey and \( v_2 \) is the speed for the return journey.

### Step 1: Identify the speeds
- Speed while walking (v1) = 8 km/h
- Speed while returning in an autorickshaw (v2) = 24 km/h

### Step 2: Substitute the values into the formula
Using the formula for average speed:

\[ \text{Average Speed} = \frac{2 \times 8 \times 24}{8 + 24} \]

### Step 3: Calculate the denominator
Calculate \( 8 + 24 \):

\[ 8 + 24 = 32 \]

### Step 4: Calculate the numerator
Calculate \( 2 \times 8 \times 24 \):

\[ 2 \times 8 = 16 \]
\[ 16 \times 24 = 384 \]

### Step 5: Divide the numerator by the denominator
Now, divide the numerator by the denominator:

\[ \text{Average Speed} = \frac{384}{32} \]

### Step 6: Perform the division
Calculate \( \frac{384}{32} \):

\[ \frac{384}{32} = 12 \]

### Conclusion
The average speed for the entire journey is **12 km/h**.

---