The price of an article is reduced by 10%. By what percent should the new price be increased to get the original price?

Question

The price of an article is reduced by 10%. By what percent should the new price be increased to get the original price?

1. A. 10%
2. B. 9 1/9%
3. C. 11 1/9% (Correct answer)
4. D. 12%

Correct Answer

Option C — C

Detailed Solution & Explanation

The correct answer is Option C.

Key Points

• Let the original price be 100.
• After a 10% reduction, the new price is 90. To return to 100, the increase needed is 10 on a base of 90:
• Increase % = (10 / 90) × 100 = 100/9 = 11 1/9 %.
• The key idea: a percentage rise and fall are taken on different bases — the fall is on 100, but the recovery rise is on 90, so the required percentage is larger than 10%.

Exam Tip

• a quick formula for restoring after an x% decrease is [x/(100 − x)] × 100 → here 10/90 × 100 = 11 1/9 %.

Additional Information

• Take the original as 100: a 10% cut gives 90, and restoring 100 needs 10 on 90 = 11.11%.
• The general formula for restoring after a fall of R% is R/(100 − R) × 100; after a rise of R%, the reduction needed is R/(100 + R) × 100.
• The asymmetry is the whole point: a 10% fall followed by a 10% rise leaves you at 99, not 100.