The taxi charges in a city contain fixed charges and additional charge/km. The charge for a distance of 10 km is Rs 350 and for 25 km is Rs 800. The charge for a distance of 30 km is:

Options

A. Rs 900
B. Rs 950
C. Rs 800
D. Rs 750

Answer

To solve the problem step by step, we will set up equations based on the information provided about taxi charges.

### 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 distance of 10 km, the total charge is Rs 350:
\[ x + 10y = 350 \quad \text{(Equation 1)} \]

2. For a distance of 25 km, the total charge is Rs 800:
\[ x + 25y = 800 \quad \text{(Equation 2)} \]

### Step 3: Subtract the Equations
To eliminate \( x \), we can subtract Equation 1 from Equation 2:
\[ (x + 25y) - (x + 10y) = 800 - 350 \]
This simplifies to:
\[ 15y = 450 \]

### Step 4: Solve for \( y \)
Now, divide both sides by 15 to find \( y \):
\[ y = \frac{450}{15} = 30 \]
So, the charge per kilometer \( y \) is Rs 30.

### Step 5: Substitute \( y \) Back to Find \( x \)
Now, substitute \( y \) back into Equation 1 to find \( x \):
\[ x + 10(30) = 350 \]
This simplifies to:
\[ x + 300 = 350 \]
Now, subtract 300 from both sides:
\[ x = 350 - 300 = 50 \]
So, the fixed charge \( x \) is Rs 50.

### Step 6: Calculate Charge for 30 km
Now that we have both \( x \) and \( y \), we can calculate the charge for a distance of 30 km:
\[ \text{Total charge} = x + 30y \]
Substituting the values of \( x \) and \( y \):
\[ \text{Total charge} = 50 + 30(30) = 50 + 900 = 950 \]

### Final Answer
The charge for a distance of 30 km is Rs 950.

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