Question

The fare of a taxi is fixed and the remaining depends on the distance covered per km. Rahim goes 30 km by a taxi and paid ₹ 400 while Kamal goes 40 km by a taxi and paid ₹ 500. Find the fixed fare and the fare per km.

Answer 1

Given:

• Rahim travels 30 km and pays ₹ 400.
• Kamal travels 40 km and pays ₹ 500.
• The taxi fare has a fixed component (fixed fare) plus a variable component depending on distance traveled (fare per km).

Let:

• Fixed fare = ₹ x
• Fare per km = ₹ y

Step-wise calculation:

1. Form equations for Rahim and Kamal:

For Rahim: Fixed fare + 30 × Fare per km = 400

x + 30y = 400   ...(Equation 1)

For Kamal: Fixed fare + 40 × Fare per km = 500

x + 40y = 500   ...(Equation 2)

2. Subtract Equation 1 from Equation 2 to eliminate x:

(x + 40y) – (x + 30y) = 500 – 400 

40y – 30y = 100 

10y = 100

⇒ y = 10

3. Substitute (y = 10) back into Equation 1 to find x: 

x + 30 × 10 = 400 

x + 300 = 400 

x = 400 – 300

x = 100

Fixed fare = ₹ 100

Fare per km = ₹ 10

So, the taxi fare consists of a fixed fare of ₹ 100 plus ₹ 10 per kilometer traveled.