Question

Sudhir purchased a chair with 3 successive discounts of 20%, 12.5% and 5%. Find the equivalent single discount.

• A. 33.5%
• B. 30%
• C. 32%
• D. 35%

Hint:

For successive discounts, never add the percentages. Always multiply the remaining price factors and subtract the result from 100% to get the equivalent single discount.

Answer 1

The Correct Option is A

Step 1: Understanding successive discounts.
Successive discounts are not added directly. Each discount is applied on the reduced price obtained after the previous discount. Therefore, to find the equivalent single discount, we use the concept of multiplying remaining price factors.
Step 2: Convert discounts into price factors.
A discount of 20% means the customer pays 80% of the marked price, so the price factor is \( 0.80 \).
A discount of 12.5% means the customer pays 87.5% of the reduced price, so the price factor is \( 0.875 \).
A discount of 5% means the customer pays 95% of the reduced price, so the price factor is \( 0.95 \).
Step 3: Multiply all price factors.
\[ \text{Net price factor} = 0.80 \times 0.875 \times 0.95 \]
Step 4: Perform the calculation step by step.
\[ 0.80 \times 0.875 = 0.70 \]
\[ 0.70 \times 0.95 = 0.665 \]
Step 5: Find the equivalent discount.
The final price paid is 66.5% of the marked price.
Therefore, the equivalent single discount is:
\[ 100% - 66.5% = 33.5% \]
Step 6: Final conclusion.
Hence, the equivalent single discount corresponding to the three successive discounts is 33.5%.