A shopkeeper charges sales tax of `x%`up to ₹2,000 and above it he charges `y%` A customer pays total tax of ₹320, when he purchases the goods worth ₹6,000 and he pay's the total tax of ₹680 for the goods worth ₹12,000. The value of (x-y) is :

Options

A. 0
B. `-2`
C. `-4`
D. 5

Answer

To solve the problem, we need to find the values of \( x \) and \( y \) based on the information provided about the sales tax charged by the shopkeeper.

### Step-by-step Solution:

1. **Understanding the Tax Structure**:
- The shopkeeper charges \( x\% \) sales tax on the first ₹2,000.
- For any amount above ₹2,000, he charges \( y\% \).

2. **Calculating the Total Tax for ₹6,000**:
- The first ₹2,000 incurs tax of \( x\% \):
\[ \text{Tax on first } 2000 = \frac{x}{100} \times 2000 = 20x \]
- The remaining amount is ₹4,000 (i.e., ₹6,000 - ₹2,000), which incurs tax of \( y\% \):
\[ \text{Tax on remaining } 4000 = \frac{y}{100} \times 4000 = 40y \]
- The total tax paid when purchasing goods worth ₹6,000 is given as ₹320:
\[ 20x + 40y = 320 \quad \text{(Equation 1)} \]

3. **Calculating the Total Tax for ₹12,000**:
- The first ₹2,000 incurs tax of \( x\% \):
\[ \text{Tax on first } 2000 = 20x \]
- The remaining amount is ₹10,000 (i.e., ₹12,000 - ₹2,000), which incurs tax of \( y\% \):
\[ \text{Tax on remaining } 10000 = \frac{y}{100} \times 10000 = 100y \]
- The total tax paid when purchasing goods worth ₹12,000 is given as ₹680:
\[ 20x + 100y = 680 \quad \text{(Equation 2)} \]

4. **Solving the Equations**:
- From Equation 1:
\[ 20x + 40y = 320 \implies x + 2y = 16 \quad \text{(Divide by 20)} \]
- From Equation 2:
\[ 20x + 100y = 680 \implies x + 5y = 34 \quad \text{(Divide by 20)} \]

5. **Subtracting the Two Equations**:
- We have:
\[ x + 5y = 34 \quad \text{(Equation 3)} \]
\[ x + 2y = 16 \quad \text{(Equation 4)} \]
- Subtract Equation 4 from Equation 3:
\[ (x + 5y) - (x + 2y) = 34 - 16 \]
\[ 3y = 18 \implies y = 6 \]

6. **Finding \( x \)**:
- Substitute \( y = 6 \) back into Equation 4:
\[ x + 2(6) = 16 \implies x + 12 = 16 \implies x = 4 \]

7. **Finding \( x - y \)**:
- Now, we calculate \( x - y \):
\[ x - y = 4 - 6 = -2 \]

### Final Answer:
The value of \( x - y \) is \( -2 \).