Question

During a film festival, a series of two successive discounts is offered on the sale of movie tickets. A discount of \(x\%\) is offered on the sale price of the ticket and an additional discount of \( x\%\) is offered on the discounted price of the ticket. If the total discount is equivalent to \(36\%\), then what is the value of \(x\)?

• A. \(17\%\)
• B. \(18\%\)
• C. \(19\%\)
• D. \(20\%\)

Answer 1

The Correct Option is D

Step 1: Let the original price of the ticket be P. The first discount of x% reduces the price to:

\[ P \times \left(1 - \frac{x}{100} \right). \]

The second discount of x% is applied to the new price: 

\[ P \times \left(1 - \frac{x}{100} \right) \times \left(1 - \frac{x}{100} \right). \]

The total price after both discounts is:

\[ P \times \left(1 - \frac{x}{100} \right)^2. \]

Step 2: The total discount is 36%, so the final price is 64% of the original price:

\[ P \times \left(1 - \frac{x}{100} \right)^2 = P \times 0.64. \]

Step 3: Dividing both sides by P:

\[ \left(1 - \frac{x}{100} \right)^2 = 0.64. \]

Taking the square root of both sides:

\[ 1 - \frac{x}{100} = 0.8 \Rightarrow \frac{x}{100} = 0.2 \Rightarrow x = 20. \]

Conclusion: The value of x is 20%.