If tax on a commodity is reduced by 10%, total revenue remains unchanged . What is the percentage increase in its consumtion ?

Options

A. `11(1)/(9)%`
B. `20%`
C. `10%`
D. `9(1)/(11)%`

Explanation

To solve the problem step by step, we will analyze the situation where the tax on a commodity is reduced by 10%, and we need to find the percentage increase in its consumption while keeping the total revenue unchanged.

### Step-by-Step Solution:

1. **Define Initial Variables:**
- Let the initial consumption be \( C_1 = 10 \) units.
- Let the initial tax be \( T_1 = 10\% \) of the price.
- Therefore, the initial revenue \( R_1 = C_1 \times T_1 = 10 \times 10 = 100 \) units.

2. **Calculate New Tax Rate:**
- The tax is reduced by 10%, so the new tax \( T_2 = T_1 - 10\% \) of \( T_1 \).
- This means \( T_2 = 10 - 1 = 9 \) units.

3. **Set Up the Equation for Unchanged Revenue:**
- Since the total revenue remains unchanged, we have:
\[ R_2 = C_2 \times T_2 = 100 \]
- Here, \( C_2 \) is the new consumption we need to find.

4. **Substituting Known Values:**
- Substitute \( T_2 \) into the revenue equation:
\[ C_2 \times 9 = 100 \]

5. **Solve for New Consumption \( C_2 \):**
- Rearranging gives:
\[ C_2 = \frac{100}{9} \text{ units} \]

6. **Calculate the Increase in Consumption:**
- The increase in consumption is given by:
\[ \text{Increase} = C_2 - C_1 = \frac{100}{9} - 10 \]
- To perform this subtraction, convert 10 into a fraction:
\[ 10 = \frac{90}{9} \]
- Thus, the increase becomes:
\[ \text{Increase} = \frac{100}{9} - \frac{90}{9} = \frac{10}{9} \text{ units} \]

7. **Calculate the Percentage Increase:**
- The percentage increase in consumption is calculated as:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase}}{C_1} \right) \times 100 = \left( \frac{\frac{10}{9}}{10} \right) \times 100 \]
- Simplifying this gives:
\[ \text{Percentage Increase} = \left( \frac{10}{90} \right) \times 100 = \frac{1000}{90} = \frac{100}{9} \approx 11.11\% \]

### Final Answer:
The percentage increase in consumption is \( \frac{100}{9} \% \) or approximately \( 11.11\% \).