A shop cuts the marked price of an article by 10%. By what exact percentage must the reduced price be increased to restore it to the original (former) price?

Introduction / Context:
This is a classic reverse-percentage question from retail mathematics. If a price is first decreased and then increased, the required percentage to return to the original value is not the same as the initial decrease. We need to compute the exact increase that undoes a 10% cut.

Given Data / Assumptions:

• Initial price (assume) = P.
• First operation: 10% reduction.
• Second operation: an unknown percentage increase that restores the price to exactly P.
• All changes are on the current price at each step (successive percentage changes).

Concept / Approach:
After a 10% cut, the new price is 90% of P, i.e., 0.9P. To get back to P, we must find r such that (1 + r) * 0.9P = P. Solving for r gives r = 1/9 = 0.111… = 11 1/9%. The key idea is that reverse percentages are computed relative to the reduced base, not the original base.

Step-by-Step Solution:

Verification / Alternative check:
Take P = 100. After 10% cut → 90. Increase by 11 1/9% → 90 * (1 + 1/9) = 90 * (10/9) = 100, which matches the original price.

Why Other Options Are Wrong:

• 11%: Slightly low; 90 * 1.11 = 99.9, not fully restored.
• 10%: Reversing 10% needs more than 10% because the base is smaller.
• 12 1/2%: Too high; would overshoot beyond the original.

Common Pitfalls:
Assuming the reverse percentage equals the original cut. Always compute on the changed base.

Final Answer: