Question

What single discount is equivalent to two successive discounts of 15% and 10%?

a) 25%
b) 20%
c) 23.5%
d) 24.5%

Answer 1

The equivalent single discount to two successive discounts of 15% and 10% is found by applying each discount sequentially to a starting value and then determining what single discount results in the same final price. The correct answer is c. 23.5%.

Step-by-step explanation:

To calculate the single discount equivalent to two successive discounts, we need to apply each discount one after the other to a base price and then determine the single percentage that would give the same final price. Let's assume the base price is $100 for easier calculation.

First, we apply a 15% discount, so we have $100 - ($100 × 0.15) = $100 - $15 = $85.

Next, we apply a 10% discount to the new price, so we have $85 - ($85 × 0.10) = $85 - $8.50 = $76.50.

Now, to find the single discount, we calculate the total reduction: $100 - $76.50 = $23.50.

The single discount equivalent to a 15% and 10% successive discount is ($23.50 / $100) × 100% = 23.5%.

Therefore, the correct answer is c. 23.5%.