On a journey across Bombay, a tourist bus averages 10 km/h for 20% of the distance, 30 km/h for 60% of it and 20 km/h for the remainder. The average speed for the whole journey was

Options

A. 10 km/h
B. 30 km/h
C. 5 km/h
D. 20 km/h

Answer

To find the average speed for the whole journey of the tourist bus, we will follow these steps:

### Step 1: Define the total distance
Let the total distance of the journey be \( D \) kilometers. For simplicity, we can assume \( D = 100 \) kilometers. This makes it easier to calculate percentages.

### Step 2: Calculate the distance for each segment
- **First segment (20% of the distance)**:
\[ \text{Distance} = 20\% \text{ of } 100 = 20 \text{ km} \]
- **Second segment (60% of the distance)**:
\[ \text{Distance} = 60\% \text{ of } 100 = 60 \text{ km} \]
- **Third segment (remaining distance)**:
\[ \text{Distance} = 100\% - (20\% + 60\%) = 20\% \text{ of } 100 = 20 \text{ km} \]

### Step 3: Calculate the time taken for each segment
- **Time for the first segment** (at 10 km/h):
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{20 \text{ km}}{10 \text{ km/h}} = 2 \text{ hours} \]
- **Time for the second segment** (at 30 km/h):
\[ \text{Time} = \frac{60 \text{ km}}{30 \text{ km/h}} = 2 \text{ hours} \]
- **Time for the third segment** (at 20 km/h):
\[ \text{Time} = \frac{20 \text{ km}}{20 \text{ km/h}} = 1 \text{ hour} \]

### Step 4: Calculate the total time for the journey
\[ \text{Total Time} = 2 \text{ hours} + 2 \text{ hours} + 1 \text{ hour} = 5 \text{ hours} \]

### Step 5: Calculate the average speed for the whole journey
The average speed is given by the total distance divided by the total time:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{100 \text{ km}}{5 \text{ hours}} = 20 \text{ km/h} \]

### Conclusion
The average speed for the whole journey was **20 km/h**.

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