Taxi charges in a city consist of fixed charges and the remaining depending upon the distance travelled in kilometres. If a man travels 80 kg, he pays ₹ 1330, and travelling 90 km, he pays ₹ 1490. Find the fixed charges and rate per km.

Explanation

To solve the problem of taxi charges, we need to set up equations based on the information provided. Let's break it down step by step.

### Step 1: Define the variables
Let:
- \( x \) = Fixed charges (in ₹)
- \( y \) = Rate per kilometer (in ₹)

### Step 2: Set up the equations based on the given information
From the problem, we have two scenarios:

1. When a man travels 80 km, he pays ₹ 1330:
\[ x + 80y = 1330 \quad \text{(Equation 1)} \]

2. When he travels 90 km, he pays ₹ 1490:
\[ x + 90y = 1490 \quad \text{(Equation 2)} \]

### Step 3: Solve the equations
We can solve these two equations simultaneously.

**Subtract Equation 1 from Equation 2:**
\[ (x + 90y) - (x + 80y) = 1490 - 1330 \]
This simplifies to:
\[ 10y = 160 \]
Now, divide both sides by 10:
\[ y = 16 \]

### Step 4: Substitute \( y \) back to find \( x \)
Now that we have \( y \), we can substitute it back into either Equation 1 or Equation 2 to find \( x \). We'll use Equation 1:
\[ x + 80(16) = 1330 \]
Calculating \( 80 \times 16 \):
\[ x + 1280 = 1330 \]
Now, subtract 1280 from both sides:
\[ x = 1330 - 1280 \]
\[ x = 50 \]

### Conclusion
Thus, the fixed charges \( x \) are ₹ 50, and the rate per kilometer \( y \) is ₹ 16.

### Summary of the Solution
- Fixed charges (x) = ₹ 50
- Rate per kilometer (y) = ₹ 16