When the price of an article is increased by `p%,` then quantity of sales decrease by `10%` but sales revenue increases by `10%` Find p.

Options

A. 20
B. `22(2)/(9)`
C. `18(2)/(11)`
D. 30

Explanation

To solve the problem step by step, we will follow the reasoning provided in the video transcript and derive the value of \( p \).

### Step-by-Step Solution:

1. **Assume the Initial Price**:
Let's assume the initial price of the article is \( 100 \) (in any currency).

**Hint**: Start with a simple number to make calculations easier.

2. **Calculate New Price After Increase**:
If the price is increased by \( p\% \), the new price can be calculated as:
\[ \text{New Price} = 100 + \frac{p}{100} \times 100 = 100 + p \]

**Hint**: Remember that increasing by \( p\% \) means adding \( \frac{p}{100} \) of the original price to the original price.

3. **Calculate New Quantity After Decrease**:
If the quantity sold decreases by \( 10\% \), the new quantity sold is:
\[ \text{New Quantity} = 100 - 10\% \text{ of } 100 = 100 - 10 = 90 \]

**Hint**: Decreasing by \( 10\% \) means subtracting \( 10\% \) of the original quantity from the original quantity.

4. **Calculate Revenue**:
The revenue before the changes is:
\[ \text{Initial Revenue} = \text{Price} \times \text{Quantity} = 100 \times 100 = 10000 \]
After the price increase and quantity decrease, the new revenue is:
\[ \text{New Revenue} = \text{New Price} \times \text{New Quantity} = (100 + p) \times 90 \]
According to the problem, the new revenue increases by \( 10\% \):
\[ \text{New Revenue} = 10000 + 10\% \text{ of } 10000 = 10000 + 1000 = 11000 \]

**Hint**: Remember that revenue is calculated as price multiplied by quantity.

5. **Set Up the Equation**:
Now we can set up the equation based on the new revenue:
\[ (100 + p) \times 90 = 11000 \]

**Hint**: This equation relates the new price and quantity to the new revenue.

6. **Solve for \( p \)**:
Expanding the equation:
\[ 9000 + 90p = 11000 \]
Rearranging gives:
\[ 90p = 11000 - 9000 \]
\[ 90p = 2000 \]
Dividing both sides by \( 90 \):
\[ p = \frac{2000}{90} = \frac{200}{9} \]

**Hint**: Isolate \( p \) by moving all other terms to the other side of the equation.

7. **Calculate the Final Value**:
To get a decimal value:
\[ p \approx 22.22 \]

**Hint**: You can convert fractions to decimals for easier interpretation.

### Final Answer:
The value of \( p \) is approximately \( 22.22\% \).