Shiva took an auto for remaining distance of his journey at 25 km/hr he had already travelled a certain distance by walking at 5 km/hr he spent 10 hours for entire journey the average speed is 17km/hr what is distance of journey travelled by auto

Options

A. 90km
B. 105km
C. 135km
D. 150km

Answer

To solve the problem, we need to break it down into steps. Here's a step-by-step solution:

### Step 1: Define Variables
Let:
- \( d_w \) = distance travelled by walking
- \( d_a \) = distance travelled by auto
- \( t_w \) = time spent walking
- \( t_a \) = time spent in auto

### Step 2: Use Given Information
From the problem, we know:
- Speed while walking = 5 km/hr
- Speed while in auto = 25 km/hr
- Total time for the journey = 10 hours
- Average speed = 17 km/hr

### Step 3: Set Up Equations
1. The total distance \( D \) can be expressed as:
\[ D = d_w + d_a \]

2. The total time can be expressed as:
\[ t_w + t_a = 10 \]

3. The time spent walking and in the auto can be expressed in terms of distance and speed:
\[ t_w = \frac{d_w}{5} \quad \text{and} \quad t_a = \frac{d_a}{25} \]

### Step 4: Substitute Time Equations
Substituting \( t_w \) and \( t_a \) into the total time equation:
\[ \frac{d_w}{5} + \frac{d_a}{25} = 10 \]

### Step 5: Express \( d_a \) in terms of \( d_w \)
To eliminate one variable, we can express \( d_a \) in terms of \( d_w \):
\[ \frac{d_a}{25} = 10 - \frac{d_w}{5} \]
Multiplying through by 25 to eliminate the fraction:
\[ d_a = 250 - 5d_w \]

### Step 6: Substitute into Total Distance Equation
Now, substitute \( d_a \) into the total distance equation:
\[ D = d_w + (250 - 5d_w) = 250 - 4d_w \]

### Step 7: Use Average Speed
The average speed is given by:
\[ \text{Average Speed} = \frac{D}{\text{Total Time}} = \frac{250 - 4d_w}{10} = 17 \]

### Step 8: Solve for \( d_w \)
Multiply both sides by 10:
\[ 250 - 4d_w = 170 \]
Rearranging gives:
\[ 4d_w = 80 \quad \Rightarrow \quad d_w = 20 \]

### Step 9: Find \( d_a \)
Now substitute \( d_w \) back into the equation for \( d_a \):
\[ d_a = 250 - 5(20) = 250 - 100 = 150 \]

### Final Answer
The distance travelled by auto is:
\[ \boxed{150 \text{ km}} \]