Question

Two successive discounts of 8% and 12% are equal to a single discount of:

• A. 19.04%
• B. 20%
• C. 20.96%
• D. 22%

Answer 1

The Correct Option is A

To find the single equivalent discount to two successive discounts of 8% and 12%, we need to use the formula for successive discounts. When two discounts of \(x\%\) and \(y\%\) are given, the equivalent single discount \(D%\) can be calculated using the formula:

\(D = x + y - \left(\frac{x \cdot y}{100}\right)\) 

Given the discounts are 8% and 12%, let's substitute these values into the formula:

\(D = 8 + 12 - \left(\frac{8 \cdot 12}{100}\right)\)

Calculate each part step-by-step:

• Add the two discounts: \(8 + 12 = 20\)
• Calculate the product of the discounts divided by 100: \(\left(\frac{8 \cdot 12}{100}\right) = \frac{96}{100} = 0.96\)
• Subtract the result from the sum of the discounts: \(20 - 0.96 = 19.04\)

Therefore, the single equivalent discount for the two successive discounts of 8% and 12% is 19.04%.

Thus, the correct answer is 19.04%.