An item is sold with a 10% discount on its marked price, and then the customer receives an additional 20% cashback on the amount actually paid.\nWhat is the overall effective discount percentage on the marked price?

Introduction / Context:
This question combines two different benefits: a price discount and a cashback. It checks whether you can track the real amount of money finally spent compared to the marked price. Many online platforms and shopping apps use similar combinations of discounts and cashbacks, so understanding this calculation has both exam and real life value.

Given Data / Assumptions:

• Marked price of the item is assumed to be M.
• First, a flat discount of 10% is applied on M.
• After that, the customer receives 20% cashback on the amount paid after the discount.
• We need the overall effective discount as a percentage of the marked price M.

Concept / Approach:
The effective discount is based on how much the customer finally spends compared to the marked price. First we calculate the discounted price. Then we calculate the cashback on this discounted amount. Finally, we subtract the cashback from the discounted price to get the net amount actually spent. The effective discount percent is then (marked price - net spend) / marked price * 100. The trick is to perform each step in the correct order and keep track of which amount each percentage applies to.

Step-by-Step Solution:
Step 1: Assume the marked price M = 100 units for simplicity.Step 2: A 10% discount gives a discounted price of 100 * (1 - 10/100) = 90 units.Step 3: Cashback is 20% of the amount paid, which is 20% of 90 units.Step 4: Cashback = 90 * 20 / 100 = 18 units.Step 5: Net amount paid by the customer = discounted price - cashback = 90 - 18 = 72 units.Step 6: Effective discount = (original marked price - net amount) / original marked price * 100 = (100 - 72) / 100 * 100 = 28 percent.

Verification / Alternative check:
We can compute in terms of M instead of 100. After a 10% discount, the customer pays 0.9 * M. Cashback is 20% of this, which is 0.2 * 0.9 * M = 0.18 * M. Net payment is 0.9 * M - 0.18 * M = 0.72 * M. Therefore, the customer effectively pays 72% of the marked price. The effective discount is 100% - 72% = 28%. This matches the numeric solution and confirms the result.

Why Other Options Are Wrong:
33.6 percent may come from incorrectly adding 10% and 20% of different bases without subtracting properly.
30 percent is a rough guess and does not match the detailed calculation of net payment.
22 percent would correspond to paying 78% of the marked price, which does not arise from the given steps.
18 percent corresponds only to the cashback amount, not the total benefit including the discount.

Common Pitfalls:
Candidates frequently add 10% and 20% directly to claim a 30% benefit or treat cashback and discount as if both were calculated on the same original base. Another mistake is to forget that cashback is money returned after payment, meaning the effective cost is less than the discounted price. A safe method is always to assume an easy marked price such as 100 units, compute each step in order, and then find the net percentage difference from that original value.

Final Answer:
The overall effective discount on the marked price is 28 percent.