The tax imposed on an article in decreased by 10% and its consumption increases by 10%. Find the percentage change in revenue from it.

Options

A. 10% increase
B. 2% decrease
C. 1% decrease
D. 11% increase

Answer

To solve the problem of finding the percentage change in revenue when the tax on an article decreases by 10% and its consumption increases by 10%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Changes**:
- The tax on the article decreases by 10%. This means if the original tax was T, the new tax will be:
\[ T' = T - 0.10T = 0.90T \]
- The consumption of the article increases by 10%. If the original quantity consumed was Q, the new quantity consumed will be:
\[ Q' = Q + 0.10Q = 1.10Q \]

2. **Calculate the Original Revenue**:
- The original revenue (R) generated from the article can be calculated as:
\[ R = T \times Q \]

3. **Calculate the New Revenue**:
- The new revenue (R') after the changes will be:
\[ R' = T' \times Q' = (0.90T) \times (1.10Q) \]
- Simplifying this gives:
\[ R' = 0.90T \times 1.10Q = 0.99TQ \]

4. **Calculate the Change in Revenue**:
- The change in revenue can be calculated as:
\[ \text{Change in Revenue} = R' - R = 0.99TQ - TQ = -0.01TQ \]

5. **Calculate the Percentage Change in Revenue**:
- The percentage change in revenue is given by:
\[ \text{Percentage Change} = \left( \frac{\text{Change in Revenue}}{\text{Original Revenue}} \right) \times 100 \]
- Substituting the values:
\[ \text{Percentage Change} = \left( \frac{-0.01TQ}{TQ} \right) \times 100 = -1\% \]

### Conclusion:
The percentage change in revenue from the article is a decrease of **1%**.

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