An item is sold at a 25% discount and the buyer also receives 10% cashback on the amount paid. What is the effective discount percentage on the marked price?

Introduction / Context:
This question involves two types of benefits given to a buyer: a discount on the marked price and a cashback on the amount actually paid. The effective discount is the total reduction in net cost to the buyer, expressed as a percentage of the original marked price. This type of mixed benefit scenario is common in modern retail promotions and is a useful application of percentage calculations.

Given Data / Assumptions:
Marked price (MP) of an item is assumed as a convenient value, say 100 units, since we work with percentages.
There is a 25 percent discount on the marked price at the time of purchase.
The buyer then receives 10 percent cashback on the amount paid after the discount.
We must find the effective discount percentage relative to the original marked price.

Concept / Approach:
First, apply the 25 percent discount to the marked price to find the initial payment. Then apply the 10 percent cashback to this payment amount. The net amount actually borne by the buyer is payment minus cashback. The effective discount is equal to marked price minus net payment, divided by marked price, multiplied by 100. Using a convenient marked price of 100 makes the calculations very straightforward, and the percentage result is independent of the assumed value.

Step-by-Step Solution:
Assume marked price MP = 100 units. First discount = 25 percent, so amount of discount = 25 percent of 100 = 25 units. Price after discount = 100 - 25 = 75 units. Cashback rate = 10 percent of the amount paid (which is 75 units). Cashback amount = 10 percent of 75 = 7.5 units. Net amount actually paid by the buyer = 75 - 7.5 = 67.5 units. Total effective discount in units = marked price - net payment = 100 - 67.5 = 32.5. Effective discount percentage = (32.5 / 100) * 100 = 32.5 percent.

Verification / Alternative check:
We can express the process via multipliers. After a 25 percent discount, the payable fraction of the marked price is 0.75. A 10 percent cashback on this payment means the buyer effectively pays 0.90 of 0.75 of the marked price, so effective payment factor = 0.75 * 0.90 = 0.675. The net payment is 67.5 percent of the marked price. Therefore, effective discount = 100 percent - 67.5 percent = 32.5 percent, confirming our earlier calculation.

Why Other Options Are Wrong:
An effective discount of 35.75 percent or 35 percent would correspond to different net payment factors that are not equal to 0.675. A discount of 12.5 percent is far too small and ignores the substantial combined effect of the original discount and cashback. Only 32.5 percent aligns with the actual net cost to the buyer after both benefits are applied.

Common Pitfalls:
One typical mistake is to simply add 25 percent and 10 percent to conclude a 35 percent discount. This is incorrect because the 10 percent cashback is computed on the reduced price, not on the original marked price. Another error is to deduct cashback directly from the marked price without passing through the discounted price. The correct approach is always to follow the chronological order: apply discount first, then compute cashback on the resulting payment, and finally compare the net amount paid with the original marked price to find the effective discount.

Final Answer:
The effective discount on the marked price is 32.5 percent.