Water tax is increased by `20%` but its consumption is decreased by `20%`. Then the increase or decrease in the expenditure of the money is .

Options

A. `4%` increase
B. `5%` decrease
C. `4%` decrease
D. No change

Answer

To solve the problem of how the increase in water tax and the decrease in consumption affect the overall expenditure, we can follow these steps:

### Step 1: Understand the Changes
- The water tax is increased by 20%.
- The consumption of water is decreased by 20%.

### Step 2: Assign a Base Value
Let's assume the original cost of water tax is `100` units (this can be any value, but using 100 makes calculations easier).

### Step 3: Calculate the New Tax Amount
- The new tax amount after a 20% increase:
\[ \text{New Tax} = 100 + (20\% \text{ of } 100) = 100 + 20 = 120 \text{ units} \]

### Step 4: Calculate the New Consumption Amount
- The new consumption amount after a 20% decrease:
\[ \text{New Consumption} = 100 - (20\% \text{ of } 100) = 100 - 20 = 80 \text{ units} \]

### Step 5: Calculate the New Expenditure
- The new expenditure can be calculated by multiplying the new tax amount by the new consumption:
\[ \text{New Expenditure} = \text{New Tax} \times \text{New Consumption} = 120 \times 80 = 9600 \text{ units} \]

### Step 6: Calculate the Original Expenditure
- The original expenditure before any changes:
\[ \text{Original Expenditure} = \text{Original Tax} \times \text{Original Consumption} = 100 \times 100 = 10000 \text{ units} \]

### Step 7: Determine the Change in Expenditure
- Now, we find the difference between the new expenditure and the original expenditure:
\[ \text{Change in Expenditure} = \text{New Expenditure} - \text{Original Expenditure} = 9600 - 10000 = -400 \text{ units} \]

### Step 8: Calculate the Percentage Change
- To find the percentage change in expenditure:
\[ \text{Percentage Change} = \left( \frac{\text{Change in Expenditure}}{\text{Original Expenditure}} \right) \times 100 = \left( \frac{-400}{10000} \right) \times 100 = -4\% \]

### Conclusion
The expenditure has decreased by 4%.

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