A taxi charges Rs 25 for the first kilometer and Rs 12.50 each for every subsequent kilometer. For a distance of p km, and amount of Rs q is paid . Which of the following shows the linear equation representing the given information ?

Options

A. 12.50 p - 12.50 = 1
B. 25-12.50 p = q
C. 25 + 12.50 p =q
D. 12.50 p + 12.50 = q

Explanation

To derive the linear equation representing the taxi fare based on the given information, we can follow these steps:

### Step 1: Understand the fare structure
The taxi fare consists of:
- Rs 25 for the first kilometer.
- Rs 12.50 for each subsequent kilometer.

### Step 2: Define the variables
Let:
- \( p \) = total distance traveled in kilometers.
- \( q \) = total amount paid in rupees.

### Step 3: Calculate the fare for the first kilometer
For the first kilometer, the fare is Rs 25.

### Step 4: Calculate the fare for subsequent kilometers
For the remaining kilometers (which is \( p - 1 \) kilometers), the fare is:
- \( 12.50 \times (p - 1) \)

### Step 5: Write the total fare equation
The total fare \( q \) can be expressed as:
\[ q = 25 + 12.50 \times (p - 1) \]

### Step 6: Simplify the equation
Now, we simplify the equation:
\[ q = 25 + 12.50p - 12.50 \]
\[ q = 12.50p + 12.50 \]

### Step 7: Rearrange the equation
We can rearrange this equation to express it in a standard linear form:
\[ 12.50p - q + 12.50 = 0 \]

### Final Linear Equation
Thus, the linear equation representing the given information is:
\[ 12.50p - q + 12.50 = 0 \]