A person claims 15 for each Kilometer which he travels by Taxi and 5 for each Kilometer when he drives his own car. If he claimed 500 for travelling 80 km, then number of Kilometer he travelled by Taxi is

Options

A. 10
B. 20
C. 30
D. 40

Answer

To solve the problem, we need to find out how many kilometers the person traveled by taxi. Let's break down the solution step by step.

### Step 1: Define Variables
Let:
- \( T \) = kilometers traveled by taxi
- \( C \) = kilometers traveled by car

### Step 2: Set Up Equations
From the problem, we know two things:
1. The total distance traveled is 80 km:
\[ T + C = 80 \quad \text{(Equation 1)} \]

2. The total claim amount is 500. The person claims 15 for each kilometer traveled by taxi and 5 for each kilometer traveled by car:
\[ 15T + 5C = 500 \quad \text{(Equation 2)} \]

### Step 3: Simplify Equation 2
To make calculations easier, we can simplify Equation 2. Divide the entire equation by 5:
\[ 3T + C = 100 \quad \text{(Equation 3)} \]

### Step 4: Solve the System of Equations
Now we have two equations:
- Equation 1: \( T + C = 80 \)
- Equation 3: \( 3T + C = 100 \)

We can subtract Equation 1 from Equation 3 to eliminate \( C \):
\[ (3T + C) - (T + C) = 100 - 80 \]
This simplifies to:
\[ 2T = 20 \]

### Step 5: Solve for \( T \)
Now, divide both sides by 2:
\[ T = \frac{20}{2} = 10 \]

### Step 6: Conclusion
The number of kilometers traveled by taxi is \( T = 10 \) km.