A shop offers a 20% discount on an item.\nIn addition, the customer applies a promo code and receives 5% cashback on the amount actually paid after the discount.\nWhat is the effective overall discount on the original marked price?

Introduction / Context:
Modern shopping frequently combines multiple offers such as discounts and cashback. Exam questions use such scenarios to test your understanding of successive percentage changes and to distinguish between a simple discount and an effective overall reduction in what the customer finally spends. Here, you must carefully combine a 20% discount and a 5% cashback to find the true effective discount on the original price.

Given Data / Assumptions:

• Let the original marked price of the item be M rupees.
• A flat 20% discount is applied first on M.
• The customer then gets 5% cashback on the amount actually paid after this discount.
• We must calculate the effective discount as a percentage of the original price M.
• Cashback is treated as money returned to the customer after payment, reducing the net amount spent.

Concept / Approach:
First, we compute the amount paid after the 20% discount. Then we calculate the cashback as 5% of that paid amount. The effective net amount spent is the discounted amount minus the cashback. Finally, the effective discount percentage is (original price - net amount spent) / original price * 100. This is different from simply adding discounts, because cashback is applied on a reduced base and acts after payment.

Step-by-Step Solution:
Step 1: After a 20% discount, the customer pays 80% of M, which is 0.80M. Step 2: Cashback is 5% of the amount paid, so cashback = 5% of 0.80M = 0.05 * 0.80M = 0.04M. Step 3: Net amount actually spent by the customer = amount paid - cashback = 0.80M - 0.04M = 0.76M. Step 4: So effectively, the customer is paying 76% of the original price. Step 5: Effective discount fraction = 1 - 0.76 = 0.24. Step 6: Effective discount percentage = 0.24 * 100 = 24 percent.

Verification / Alternative check:
Assume a concrete value, say M = Rs. 100. After a 20% discount, the customer pays Rs. 80. Cashback is 5% of 80, which is Rs. 4. Net spending = 80 - 4 = Rs. 76. Compared to the original Rs. 100, the effective reduction is 100 - 76 = Rs. 24, which is 24 percent of the original price. This numerical check confirms the algebraic reasoning.

Why Other Options Are Wrong:
25.2 percent: This would come from incorrectly adding 20% and 5% of 80 directly as if both were discounts on M, which is not how the offer works.
25 percent: A simple sum 20% + 5% ignores the fact that cashback is calculated on the reduced price, not on the original price.
6 percent: This misinterprets 5% cashback as just 1% more than a 5% discount; it ignores the main 20% reduction entirely.
23 percent: This is a rounding or approximation error; the exact calculation clearly shows 24 percent.

Common Pitfalls:
Students often simply add 20% and 5% and answer 25 percent, assuming both are equivalent discounts on the original price. Others may treat cashback as a regular discount before payment and multiply wrong bases. Always pay attention to the order and base of each percentage: the first discount is on M, the cashback is on the discounted payment, and the final effective discount is compared back to M.

Final Answer:
The effective overall discount on the original marked price is 24 percent.