Giving two successive discounts of 20% on the marked price of an article is equivalent to giving a single discount of what percentage on the original marked price?

Introduction / Context:
This is another example of combining successive percentage discounts into a single equivalent discount. It reinforces the idea that percentage changes are multiplicative. Instead of adding the percentages, we must find the combined effect on the final price and then convert that back into one effective discount rate.

Given Data / Assumptions:

• First discount = 20% on the marked price.
• Second discount = 20% on the reduced price after the first discount.
• We must find the single discount percentage that gives the same final price.
• The actual marked price does not matter because the result is percentage based.

Concept / Approach:
A discount of d% leaves (1 - d/100) of the original price. For successive discounts of 20% and 20%, the remaining fraction after both discounts is (0.80) * (0.80). The final fraction of the original price can then be expressed as (1 - D/100), where D is the single equivalent discount. We compute the product, subtract from 1, and obtain D.

Step-by-Step Solution:
Step 1: After a 20% discount, 80% of the price is left, so the factor is 0.80. Step 2: The second 20% discount again leaves 80% of the current price, with factor 0.80. Step 3: Combined factor after both discounts = 0.80 * 0.80 = 0.64. Step 4: This means the final price is 64% of the original marked price. Step 5: Therefore, total effective discount = 100% - 64% = 36%. Step 6: So a single discount of 36% is equivalent to two successive discounts of 20% each.

Verification / Alternative check:
Assume a convenient marked price, say Rs 100. After the first 20% discount, the price becomes 80. After the second 20% discount, the price becomes 80 - 16 = 64. Thus the final price is Rs 64, which is 36 less than 100, confirming that the overall discount is 36%.

Why Other Options Are Wrong:

• 40: This is obtained by incorrectly adding the two 20% discounts, which ignores the change of base.
• 44: This would be the discount if the final fraction was 56%, which is not the case here.
• 50: This is far too large and bears no relation to the correct product of factors.
• 32: This indicates a misunderstanding of how the combined discount works, possibly from subtracting 4 from 36.

Common Pitfalls:
Many students simply add 20% and 20% to claim a 40% overall discount, which is wrong because each 20% is on a different base. Others may compute the product correctly but forget to subtract from 1 to get the discount. Whenever dealing with successive percentage changes, it is best to think in terms of decimal multipliers applied one after another.

Final Answer:
Two successive discounts of 20% each are equivalent to a single discount of 36% on the original marked price.