The autorickshaw fare consists of a fixed charge together with the charge for the distance covered. For a journey of 10 km, the charge paid is 85 and for a journey of 15 km, the charge paid is 120. The fare for a journey of 25 km will be

Options

A. 175
B. 190
C. 180
D. 225

Answer

To solve the problem of finding the fare for a journey of 25 km based on the given information, we can set up a linear equation. The fare consists of a fixed charge plus a variable charge per kilometer traveled.

### Step-by-Step Solution:

1. **Define Variables**:
Let \( F \) be the fixed charge and \( C \) be the charge per kilometer.

2. **Set Up Equations**:
From the information provided:
- For a journey of 10 km, the total fare is 85:
\[ F + 10C = 85 \quad \text{(Equation 1)} \]
- For a journey of 15 km, the total fare is 120:
\[ F + 15C = 120 \quad \text{(Equation 2)} \]

3. **Solve the Equations**:
We can solve these two equations simultaneously.

- First, subtract Equation 1 from Equation 2:
\[ (F + 15C) - (F + 10C) = 120 - 85 \]
This simplifies to:
\[ 5C = 35 \]
Dividing both sides by 5 gives:
\[ C = 7 \]

4. **Find the Fixed Charge**:
Now that we have \( C \), we can substitute it back into either equation to find \( F \). Using Equation 1:
\[ F + 10(7) = 85 \]
Simplifying this gives:
\[ F + 70 = 85 \]
Therefore:
\[ F = 85 - 70 = 15 \]

5. **Calculate the Fare for 25 km**:
Now that we have both \( F \) and \( C \):
\[ \text{Fare for 25 km} = F + 25C \]
Substituting the values:
\[ \text{Fare for 25 km} = 15 + 25(7) = 15 + 175 = 190 \]

### Final Answer:
The fare for a journey of 25 km will be **190**.