Comparing year-over-year changes: Sales decreased by 80% from 2008 to 2009. If sales in 2010 returned to the 2008 level, by what percentage did sales increase from 2009 to 2010?

Introduction / Context:
This problem shows the asymmetry of percentage increase and decrease. A large fall followed by a recovery to the original base can imply a very large percentage increase, because the reference base (the lower intermediate value) is smaller.

Given Data / Assumptions:

• Let 2008 sales = S.
• 2009 sales = S decreased by 80% ⇒ 0.20S.
• 2010 sales = back to S.

Concept / Approach:
Percentage increase from 2009 to 2010 is (New − Old)/Old * 100%. Here, (S − 0.20S)/0.20S = 0.80S/0.20S = 4 ⇒ 400% increase.

Step-by-Step Solution:

Verification / Alternative check:
Numeric check: If S = 100 units, 2009 = 20 units. Jump to 100 units is a gain of 80 units; 80/20 * 100% = 400%.

Why Other Options Are Wrong:

• 80%, 100%, 120%: Underestimate the increase because they compare to the wrong base (often mistakenly to the original S rather than the reduced 0.20S).

Common Pitfalls:
Assuming the recovery percentage equals the initial drop (80%). Reverse changes are computed relative to the new base, not the old one.

Final Answer: