A man goes from Kalyan to Mumbai at the rate of 10 kmph and returns to Kalyan at the rate of 15kmph. What is his aveage speed during the whole journey?

Options

A. 56km/hr
B. 15km/h
C. 42km/h
D. 12km/h

Answer

To find the average speed of the man during his whole journey from Kalyan to Mumbai and back, we can use the formula for average speed when the distances are the same but the speeds differ. The formula is:

\[ \text{Average Speed} = \frac{2ab}{a + b} \]

where \(a\) is the speed for the first part of the journey, and \(b\) is the speed for the return journey.

### Step-by-step Solution:

1. **Identify the speeds**:
- Speed from Kalyan to Mumbai (a) = 10 km/h
- Speed from Mumbai to Kalyan (b) = 15 km/h

2. **Plug the values into the formula**:
\[ \text{Average Speed} = \frac{2 \times 10 \times 15}{10 + 15} \]

3. **Calculate the denominator**:
\[ 10 + 15 = 25 \]

4. **Calculate the numerator**:
\[ 2 \times 10 \times 15 = 300 \]

5. **Divide the numerator by the denominator**:
\[ \text{Average Speed} = \frac{300}{25} = 12 \text{ km/h} \]

Thus, the average speed during the whole journey is **12 km/h**.