Question

A merchant offers a large group of items at 30% off. Later, the merchant takes 20% off these sale prices and claims that the final price of these items is 50% off the original price. As a percentage of the original price, what is the difference between the true discount and the merchant's claimed discount? (Your answer should be a positive difference.)

a) 5%
b) 10%
c) 15%
d) 20%

Answer 1

The true discount is 44% after applying a 30% discount followed by a 20% discount on the reduced sale price. The merchant's claimed discount of 50% is an overstatement. The actual percentage difference between the true discount and the claimed discount is 6%, with the closest option being 5% (Option a).

Step-by-step explanation:

To determine the true discount compared to the merchant's claimed discount, we need to calculate the successive percentage discounts. The merchant offers items at 30% off, and then a further 20% off the reduced price. We can calculate the compound discount using the original price as a base:

• After 30% discount: $1.00 - $0.30 = $0.70
• After additional 20% discount on the reduced price: $0.70 - ($0.70 × 0.20) = $0.70 - $0.14 = $0.56

The final price is 56% of the original price, so the true discount is 44%. The merchant's claimed discount is 50%. Therefore, the difference between the true discount and the claimed discount is:

50% - 44% = 6%

The closest option from the given choices to the actual percentage difference of 6% is 5% (Option a).