Mr. Bundda travels in his car and covers 1/4 parts of his journey with 8 km/h , 3/5 part with 6 km/h and remaining 3/20 part with a speed of 10 km/h . Find out his average speed during the whole journey .

Options

A. 6.83 km/h
B. 9 km/h
C. 4 km/h
D. 8.5 km/h

Answer

To find Mr. Bundda's average speed during his journey, we will follow these steps:

### Step 1: Define the total distance
Let the total distance of the journey be \( x \) kilometers.

### Step 2: Calculate the distance for each part of the journey
- The first part of the journey is \( \frac{1}{4} \) of \( x \):
\[ \text{Distance}_1 = \frac{1}{4}x \]

- The second part of the journey is \( \frac{3}{5} \) of \( x \):
\[ \text{Distance}_2 = \frac{3}{5}x \]

- The remaining part of the journey is \( \frac{3}{20} \) of \( x \):
\[ \text{Distance}_3 = \frac{3}{20}x \]

### Step 3: Calculate the time taken for each part
Using the formula \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \):

- For the first part:
\[ \text{Time}_1 = \frac{\frac{1}{4}x}{8} = \frac{x}{32} \text{ hours} \]

- For the second part:
\[ \text{Time}_2 = \frac{\frac{3}{5}x}{6} = \frac{3x}{30} = \frac{x}{10} \text{ hours} \]

- For the third part:
\[ \text{Time}_3 = \frac{\frac{3}{20}x}{10} = \frac{3x}{200} \text{ hours} \]

### Step 4: Calculate the total time taken for the journey
Now, we will sum up all the times:
\[ \text{Total Time} = \text{Time}_1 + \text{Time}_2 + \text{Time}_3 = \frac{x}{32} + \frac{x}{10} + \frac{3x}{200} \]

To add these fractions, we need a common denominator. The least common multiple (LCM) of 32, 10, and 200 is 400.

- Convert each fraction:
\[ \frac{x}{32} = \frac{12.5x}{400} \]
\[ \frac{x}{10} = \frac{40x}{400} \]
\[ \frac{3x}{200} = \frac{6x}{400} \]

Now, adding these:
\[ \text{Total Time} = \frac{12.5x + 40x + 6x}{400} = \frac{58.5x}{400} = \frac{117x}{800} \]

### Step 5: Calculate the average speed
The average speed is given by the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{x}{\frac{117x}{800}} = \frac{800}{117} \text{ km/h} \]

### Step 6: Simplify the average speed
Calculating \( \frac{800}{117} \) gives approximately \( 6.83 \) km/h.

Thus, Mr. Bundda's average speed during the whole journey is approximately **6.83 km/h**.

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