Two successive discounts of 10% and 20% are offered on the marked price of an article.\nWhat single equivalent discount percentage would give the same final selling price as these two successive discounts together?

Introduction / Context:
This aptitude question tests the concept of successive discounts and how to convert them into a single equivalent discount percentage. Many students simply add percentages, which is incorrect when more than one discount is applied one after another. Understanding the correct method is very important for percentage based questions in competitive exams and everyday shopping scenarios.

Given Data / Assumptions:

• First discount = 10% on the marked price.
• Second discount = 20% on the already discounted price.
• We assume the same marked price throughout the calculation.
• We need one single discount that produces the same final selling price.

Concept / Approach:
The key idea is that successive discounts multiply their remaining price factors. If a discount is d%, the remaining price factor is (1 - d/100). The combined remaining factor of two discounts is the product of the two separate remaining factors. Once this combined factor is known, we compare it with the original price to find the single equivalent discount percentage.

Step-by-Step Solution:
Step 1: Assume the marked price is 100 units for simplicity.Step 2: After the first discount of 10%, remaining price = 100 * (1 - 10/100) = 100 * 0.9 = 90 units.Step 3: After the second discount of 20% on 90, remaining price = 90 * (1 - 20/100) = 90 * 0.8 = 72 units.Step 4: The final price is 72 units when the marked price was 100 units.Step 5: The single equivalent discount = (100 - 72) percent = 28 percent.

Verification / Alternative check:
Another way is to work directly with factors. First discount 10% gives factor 0.9. Second discount 20% gives factor 0.8. Combined factor = 0.9 * 0.8 = 0.72. A single discount that leaves 0.72 of the price must be 1 - 0.72 = 0.28 or 28%. This matches our earlier result, so the answer is consistent.

Why Other Options Are Wrong:
27% is too small because the remaining price would be 73 units, not 72 units.
25% discount gives a final price of 75 units, which is higher than 72 units, so it is incorrect.
30% discount leaves only 70 units, which is lower than 72 units, so it is not equivalent.
22% is even smaller discount and clearly does not match a final price of 72 units.

Common Pitfalls:
A very common mistake is to simply add 10% and 20% to get 30%. This ignores the fact that the second discount is not on the original price but on the already reduced price. Another error is to forget to assume a convenient marked price such as 100 units, which makes calculations straightforward. Students should remember that when multiple percentage changes are applied successively, they must be converted into decimal factors, multiplied, and then converted back into a single percentage change.

Final Answer:
The capacity of a single discount equivalent to successive discounts of 10% and 20% is a discount of 28% on the marked price.