Equivalent single discount from a series Find the single equivalent discount for the successive series: 10%, then 20%, then 40%.

Introduction / Context:
Successive discounts multiply the retained fractions of price, not the percentages directly. The single equivalent discount is 1 minus the product of retention factors.

Given Data / Assumptions:

• Discounts: 10%, 20%, 40% applied successively.

Concept / Approach:
Retention after each discount: 90% = 0.90, then 80% = 0.80, then 60% = 0.60. Multiply to get overall retention; subtract from 1 for the net discount.

Step-by-Step Solution:
Overall retention = 0.90 × 0.80 × 0.60 = 0.432.Equivalent single discount = 1 − 0.432 = 0.568 = 56.8%.

Verification / Alternative check:
If marked price is 100, final price after series = 100 × 0.432 = 43.2, so discount = 56.8, i.e., 56.8%.

Why Other Options Are Wrong:
50% and 70% ignore compounding; 70.28% is not the product-based result; 60% is a rough guess, not exact.

Common Pitfalls:
Adding discounts arithmetically (10 + 20 + 40 = 70) instead of compounding multiplicatively.

Final Answer:
56.80%