On increasing the price of tickets for a show by 20 % the audience decreases by 30%. What is the effect on revenue?

Options

A. 4% decrease
B. 4% increase
C. 16% decrease
D. 16% increase

Answer

To solve the problem of how the increase in ticket price and the decrease in audience affects revenue, we can follow these steps:

### Step 1: Identify the percentage increase and decrease
- The ticket price is increased by 20%, so the percentage increase (P) is 20%.
- The audience decreases by 30%, so the percentage decrease (Q) is 30%.

### Step 2: Use the revenue effect formula
The formula to calculate the effect on revenue is:
\[ \text{Effect on Revenue} = P - Q - \left(\frac{P \times Q}{100}\right) \]
Where:
- \(P\) = percentage increase
- \(Q\) = percentage decrease

### Step 3: Substitute the values into the formula
Substituting the values we have:
\[ \text{Effect on Revenue} = 20 - 30 - \left(\frac{20 \times 30}{100}\right) \]

### Step 4: Calculate the product of percentage increase and decrease
Calculating \( \frac{20 \times 30}{100} \):
\[ \frac{20 \times 30}{100} = \frac{600}{100} = 6 \]

### Step 5: Substitute back into the formula
Now substituting back into the formula:
\[ \text{Effect on Revenue} = 20 - 30 - 6 \]

### Step 6: Perform the arithmetic
Calculating the above expression:
\[ 20 - 30 = -10 \]
\[ -10 - 6 = -16 \]

### Step 7: Interpret the result
The result is -16, which indicates that the revenue has decreased by 16%.

### Final Answer
Thus, the revenue decreased by 16%.

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