Profit and Loss – Equivalent single discount from a series: Three successive discounts of 10%, 20%, and 40% are offered. What single discount is equivalent to this series?

Introduction / Context:
Successive discounts multiply their remaining-value factors. The equivalent single discount is one minus the product of the factors. This prevents overestimating by simple addition.

Given Data / Assumptions:

• Discounts: 10%, 20%, and 40%

Concept / Approach:
Remaining-value factors: 0.90, 0.80, and 0.60. Multiply them to get the net remaining fraction; then subtract from 1 to get the equivalent single discount.

Step-by-Step Solution:
Net remaining fraction = 0.90 * 0.80 * 0.60 = 0.432Equivalent single discount = 1 − 0.432 = 0.568 = 56.8%

Verification / Alternative check:
Applying a single 56.8% discount leaves 43.2% of price, same as the product 0.432.

Why Other Options Are Wrong:
50% and 60% are round but incorrect; 70.28% is much too high; 48% is too low.

Common Pitfalls:
Adding 10 + 20 + 40 = 70% which is invalid for successive discounts.

Final Answer:
56.8%