The taxi charges in a city contain fixed charges and additional charge per kilometre. The fixed charge is for a distance of upto 5 km and additional charge per kilometre there after. 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 800
B. Rs 750
C. Rs 900
D. Rs 950

Answer

To solve the problem, we need to determine the fixed charge and the additional charge per kilometer for the taxi service based on the given information.

### Step-by-step Solution:

1. **Define Variables**:
- Let \( F \) be the fixed charge for the first 5 km.
- Let \( C \) be the additional charge per kilometer after the first 5 km.

2. **Set Up Equations**:
- From the information given:
- For a distance of 10 km, the total charge is Rs 350.
- The charge for the first 5 km is \( F \).
- The charge for the next 5 km (from 5 km to 10 km) is \( 5C \).
- Therefore, the equation is:
\[ F + 5C = 350 \quad \text{(1)} \]

- For a distance of 25 km, the total charge is Rs 800.
- The charge for the first 5 km is \( F \).
- The charge for the next 20 km (from 5 km to 25 km) is \( 20C \).
- Therefore, the equation is:
\[ F + 20C = 800 \quad \text{(2)} \]

3. **Solve the Equations**:
- We have two equations:
- \( F + 5C = 350 \) (1)
- \( F + 20C = 800 \) (2)

- Subtract equation (1) from equation (2):
\[ (F + 20C) - (F + 5C) = 800 - 350 \]
\[ 15C = 450 \]
\[ C = 30 \]

- Now substitute \( C \) back into equation (1) to find \( F \):
\[ F + 5(30) = 350 \]
\[ F + 150 = 350 \]
\[ F = 350 - 150 = 200 \]

4. **Calculate the Charge for 30 km**:
- For a distance of 30 km:
- The charge for the first 5 km is \( F = 200 \).
- The charge for the next 25 km (from 5 km to 30 km) is \( 25C = 25 \times 30 = 750 \).
- Therefore, the total charge for 30 km is:
\[ \text{Total Charge} = F + 25C = 200 + 750 = 950 \]

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

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