Successive discounts: Two successive discounts of 20% and 20% are equivalent to what single discount percentage on the list price?

Introduction / Context:
Successive discounts multiply their remaining-price factors. A discount of d% keeps (1 − d/100) of the price. Two discounts combine by multiplying these factors, then the overall discount is 1 minus the product.

Given Data / Assumptions:

• First discount = 20% ⇒ retention factor = 0.80
• Second discount = 20% ⇒ retention factor = 0.80

Concept / Approach:
Equivalent single discount D satisfies (1 − D) = 0.80 * 0.80. Compute the product and convert back to a percentage discount.

Step-by-Step Solution:
Retention after both = 0.80 * 0.80 = 0.64Equivalent single discount D = 1 − 0.64 = 0.36 = 36%

Verification / Alternative check:
On a ₹100 item: after 20% off → ₹80; second 20% off → ₹64. A single 36% off of ₹100 also gives ₹64.

Why Other Options Are Wrong:
40% simply adds 20 + 20, which is incorrect for successive discounts. 42% and 34% do not match the multiplicative outcome.

Common Pitfalls:
Adding percentages directly for successive reductions. Always multiply retention factors.

Final Answer:
36%