Equivalent single discount: Successive discounts of 10%, 20%, and 30% are equivalent to what single discount percentage?

Introduction / Context:Multiple successive discounts compound multiplicatively via retention factors. Compute the compounded retention, then convert back to a single overall discount percentage.

Given Data / Assumptions:

• Discounts: 10%, 20%, 30%
• Retention factors: 0.90, 0.80, 0.70 respectively

Concept / Approach:Overall retention = 0.90 * 0.80 * 0.70. Overall discount = 1 − overall retention. Convert to percent with one decimal place as appropriate.

Step-by-Step Solution:Retention = 0.90 * 0.80 * 0.70 = 0.504Equivalent discount = 1 − 0.504 = 0.496 = 49.6%

Verification / Alternative check:Test with ₹100: after successive cuts, price becomes ₹50.40, so the total reduction is ₹49.60, i.e., 49.6%.

Why Other Options Are Wrong:60% adds the percentages; 40.5% or 36% underestimates; 54% overestimates relative to the multiplicative rule.

Common Pitfalls:Adding the percentages directly or rounding early; compute the product first, then subtract from 1.

Final Answer:49.6%