Pankaj walked at 5 km/h for certain part of the journey and then he took an auto for the remaining part of the journey travelling at 25 km/h if he took 10 hours for the entire journey.What part of jopurney did he travelled by auto if the average speed of the entire journey be 17 km/h:

Options

A. 750 km
B. 100 km
C. 150 km
D. 200 km

Answer

To solve the problem step by step, we will use the concept of average speed and the relationship between speed, time, and distance.

### Step-by-Step Solution:

1. **Understanding the Problem**:
Pankaj walked at a speed of 5 km/h for part of the journey and then took an auto at a speed of 25 km/h for the remaining part. The total time for the journey was 10 hours, and the average speed for the entire journey was 17 km/h.

2. **Setting Up the Equation for Average Speed**:
The average speed is given by the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]
We know the average speed (17 km/h) and the total time (10 hours), so we can find the total distance:
\[ \text{Total Distance} = \text{Average Speed} \times \text{Total Time} = 17 \, \text{km/h} \times 10 \, \text{h} = 170 \, \text{km} \]

3. **Letting Variables Represent Distances**:
Let \( d_1 \) be the distance walked at 5 km/h, and \( d_2 \) be the distance traveled by auto at 25 km/h. We have:
\[ d_1 + d_2 = 170 \, \text{km} \quad \text{(1)} \]

4. **Setting Up Time Equations**:
The time taken to walk \( d_1 \) is:
\[ t_1 = \frac{d_1}{5} \quad \text{(2)} \]
The time taken to travel \( d_2 \) by auto is:
\[ t_2 = \frac{d_2}{25} \quad \text{(3)} \]
The total time is given as 10 hours:
\[ t_1 + t_2 = 10 \quad \text{(4)} \]

5. **Substituting Time Equations into Total Time**:
Substitute equations (2) and (3) into (4):
\[ \frac{d_1}{5} + \frac{d_2}{25} = 10 \]
To eliminate the fractions, multiply through by 25:
\[ 5d_1 + d_2 = 250 \quad \text{(5)} \]

6. **Solving the System of Equations**:
Now we have a system of equations:
- From (1): \( d_1 + d_2 = 170 \)
- From (5): \( 5d_1 + d_2 = 250 \)

We can subtract equation (1) from equation (5):
\[ (5d_1 + d_2) - (d_1 + d_2) = 250 - 170 \]
Simplifying gives:
\[ 4d_1 = 80 \implies d_1 = 20 \, \text{km} \]

7. **Finding \( d_2 \)**:
Substitute \( d_1 \) back into equation (1):
\[ 20 + d_2 = 170 \implies d_2 = 150 \, \text{km} \]

8. **Conclusion**:
The distance traveled by auto is \( d_2 = 150 \, \text{km} \).

### Final Answer:
Pankaj traveled **150 km** by auto.

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