The price of an article is first decreased by 10%. By what percentage must the new reduced price be increased so that the price is restored to its original value?

Introduction / Context:
This problem is a classic example of successive percentage changes where a decrease followed by an increase does not cancel out using the same percentage. It tests understanding of how percentage changes are applied on different bases. Many candidates wrongly assume that a 10% increase will undo a 10% decrease, which is not correct.

Given Data / Assumptions:
- The original price of an article is some amount, say P.
- The price is decreased by 10 percent, giving a new reduced price.
- We must find the percentage by which this reduced price should be increased to get back to P.

Concept / Approach:
A percentage decrease or increase is always calculated on the current value, not on the original value, unless explicitly stated. When the price is decreased by 10%, the new price is 90% of the original. To return to the original price, we need to increase this reduced price by a certain percentage. This required percentage can be found using ratios or by setting up a simple equation, then converting the ratio back into a percentage.

Step-by-Step Solution:
Let the original price be P. After a 10% decrease, the new price is P * (1 - 10 / 100) = P * 0.90. Call this new price P_new = 0.90P. We now increase P_new by some unknown percentage r to get back to P. So, P = P_new * (1 + r / 100) = 0.90P * (1 + r / 100). Divide both sides by P: 1 = 0.90 * (1 + r / 100). Therefore, 1 / 0.90 = 1 + r / 100. Compute 1 / 0.90 = 10 / 9. So, 10 / 9 = 1 + r / 100. Hence, r / 100 = 10 / 9 - 1 = 1 / 9. Thus, r = 100 * (1 / 9) = 100 / 9 = 11 1/9 percent.

Verification / Alternative check:
Take a simple number for the original price, such as P = 100. After 10% decrease, the new price becomes 90. To know the increase required to go from 90 back to 100, compute the difference 100 - 90 = 10. Now express this as a percentage of 90: (10 / 90) * 100 = 100 / 9 = 11 1/9 percent. This numerical approach confirms the algebraic result.

Why Other Options Are Wrong:
9 1/11%: This is a common distractor but does not satisfy the equation needed to return to the original price.
10%: This assumes that a 10% increase cancels a 10% decrease, which is incorrect because the bases are different.
11%: Close to the true answer but slightly less; it would not fully restore the original price.
12%: This overshoots and would make the price higher than the original value.

Common Pitfalls:
The main mistake is thinking that percentage increases and decreases are symmetric. Decreasing by 10% and then increasing by 10% does not bring you back to the starting point. Another error is forgetting that the second percentage is applied on the reduced amount, not on the original. Learning this idea is essential for dealing with successive discount, profit, and loss questions.

Final Answer:
To restore the original price after a 10% decrease, the new price must be increased by 11 1/9 percent.