Einstein goes from Ahemdabad to lucknow at the speed of 40 km/hr and returned at the speed of 60km/hr . The average speed of einstein during the whole journey is :

Options

A. 48 km/hr
B. 24 km/hr
C. 50 km/hr
D. None of the above

Explanation

To find the average speed of Einstein during his whole journey from Ahmedabad to Lucknow and back, we can use the formula for average speed when the distances are the same but the speeds are different.

### Step-by-Step Solution:

1. **Identify the Speeds**:
- Speed from Ahmedabad to Lucknow (A to B) = 40 km/hr
- Speed from Lucknow to Ahmedabad (B to A) = 60 km/hr

2. **Use the Average Speed Formula**:
The formula for average speed when the distance is the same for both legs of the journey is given by:
\[ \text{Average Speed} = \frac{2 \times A \times B}{A + B} \]
where A is the speed for the first part of the journey and B is the speed for the return journey.

3. **Substitute the Values**:
Here, A = 40 km/hr and B = 60 km/hr.
\[ \text{Average Speed} = \frac{2 \times 40 \times 60}{40 + 60} \]

4. **Calculate the Denominator**:
\[ 40 + 60 = 100 \]

5. **Calculate the Numerator**:
\[ 2 \times 40 \times 60 = 4800 \]

6. **Final Calculation**:
\[ \text{Average Speed} = \frac{4800}{100} = 48 \text{ km/hr} \]

### Conclusion:
The average speed of Einstein during the whole journey is **48 km/hr**.

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