A private taxi company charges a fixed charge along with a per kilometre charge based on the distance covered. For a journey of 24 km, the charges paid are Rs. 368 and for a journey of 32 km, the charges paid Rs. 464. How much will a person have to pay for travelling a distance of 15 km?

Options

A. Rs. 180
B. Rs. 260
C. Rs. 290
D. Rs. 280

Answer

To solve the problem step by step, we will define the fixed charge and the per kilometer charge, and then set up equations based on the information given.

### Step 1: Define Variables
Let:
- \( X \) = Fixed charge (in Rs.)
- \( Y \) = Charge per kilometer (in Rs.)

### Step 2: Set Up Equations
From the information given:
1. For a journey of 24 km, the total charge is Rs. 368:
\[ X + 24Y = 368 \quad \text{(Equation 1)} \]

2. For a journey of 32 km, the total charge is Rs. 464:
\[ X + 32Y = 464 \quad \text{(Equation 2)} \]

### Step 3: Solve the Equations
To eliminate \( X \), we can subtract Equation 1 from Equation 2:
\[ (X + 32Y) - (X + 24Y) = 464 - 368 \]
This simplifies to:
\[ 8Y = 96 \]
Now, divide both sides by 8:
\[ Y = 12 \quad \text{(Charge per kilometer)} \]

### Step 4: Substitute \( Y \) Back to Find \( X \)
Now we can substitute \( Y = 12 \) back into Equation 1 to find \( X \):
\[ X + 24(12) = 368 \]
Calculating \( 24 \times 12 \):
\[ X + 288 = 368 \]
Subtract 288 from both sides:
\[ X = 368 - 288 \]
\[ X = 80 \quad \text{(Fixed charge)} \]

### Step 5: Calculate the Charge for 15 km
Now, we can find the total charge for a journey of 15 km:
\[ \text{Total charge} = X + 15Y \]
Substituting the values of \( X \) and \( Y \):
\[ \text{Total charge} = 80 + 15(12) \]
Calculating \( 15 \times 12 \):
\[ \text{Total charge} = 80 + 180 \]
\[ \text{Total charge} = 260 \]

### Final Answer
The total charge for traveling a distance of 15 km is **Rs. 260**.

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