Sri krishna took the chariot and started his journey from mathura to gokul by his chariot at the speed of 40 km/hr nad then the same distance he travelled on his foot at the speed of 10km/hr from gokul to brindaban . Then he returned from brindanban to mathura via gokul at the speed of 24 km/hr riding on the horse . The average speed of the whole trip is :

Options

A. 20km/hr
B. 25 km/hr
C. 19.2 km/hr
D. 18.5 km/hr

Explanation

To find the average speed of Sri Krishna's entire trip, we will use the formula for average speed, which is given by:

\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]

### Step 1: Define the distances
Let's assume the distance from Mathura to Gokul is \(D\) km. Therefore, the distance from Gokul to Vrindavan is also \(D\) km.

### Step 2: Calculate the total distance
The total distance for the entire trip is:
- From Mathura to Gokul: \(D\)
- From Gokul to Vrindavan: \(D\)
- From Vrindavan back to Mathura via Gokul: \(D + D = 2D\)

Thus, the total distance \( = D + D + 2D = 4D\).

### Step 3: Calculate the time taken for each segment
1. **From Mathura to Gokul**:
- Speed = 40 km/hr
- Time = Distance / Speed = \( \frac{D}{40} \) hours

2. **From Gokul to Vrindavan**:
- Speed = 10 km/hr
- Time = Distance / Speed = \( \frac{D}{10} \) hours

3. **From Vrindavan back to Mathura via Gokul**:
- Speed = 24 km/hr
- Total distance = \(2D\)
- Time = Distance / Speed = \( \frac{2D}{24} = \frac{D}{12} \) hours

### Step 4: Calculate the total time
Now, we can sum up the time taken for each segment:
\[ \text{Total Time} = \frac{D}{40} + \frac{D}{10} + \frac{D}{12} \]

To add these fractions, we need a common denominator. The least common multiple of 40, 10, and 12 is 120.

- Convert each term:
- \( \frac{D}{40} = \frac{3D}{120} \)
- \( \frac{D}{10} = \frac{12D}{120} \)
- \( \frac{D}{12} = \frac{10D}{120} \)

Now, adding these:
\[ \text{Total Time} = \frac{3D}{120} + \frac{12D}{120} + \frac{10D}{120} = \frac{25D}{120} = \frac{5D}{24} \text{ hours} \]

### Step 5: Calculate the average speed
Now we can substitute the total distance and total time into the average speed formula:
\[ \text{Average Speed} = \frac{4D}{\frac{5D}{24}} = 4D \times \frac{24}{5D} = \frac{96}{5} = 19.2 \text{ km/hr} \]

### Final Answer
The average speed of the whole trip is **19.2 km/hr**.

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