Equivalent single discount for three successive discounts What single discount is equivalent to successive discounts of 10%, 20%, and 30%?

Introduction / Context:
To replace multiple successive discounts with a single equivalent discount, compute the final price factor by multiplying the remaining percentages and then convert back to a net discount from the list price.

Given Data / Assumptions:

• Successive discounts: 10%, 20%, 30%.

Concept / Approach:
Remaining price factor after discounts d1, d2, d3 is (1 − d1) * (1 − d2) * (1 − d3). The equivalent single discount D satisfies (1 − D) = that product. Thus D = 1 − product.

Step-by-Step Solution:
Remaining factors: 0.90, 0.80, 0.70.Product = 0.90 * 0.80 * 0.70 = 0.504.Equivalent discount D = 1 − 0.504 = 0.496 = 49.6%.

Verification / Alternative check:
Assuming list price 100, final price becomes 100 * 0.504 = 50.4, so discount = 100 − 50.4 = 49.6, confirming the result.

Why Other Options Are Wrong:
60% and 40.5% come from adding or partially adding discounts; 36% is unrelated; 52% is an overestimate.

Common Pitfalls:
Adding percentages directly. Always multiply remaining price factors for successive discounts.

Final Answer:
49.6 %