The marked price of an item is Rs. 500.\nIf a customer buys 2 items, a discount of 8% is given on the total marked price.\nIf a customer buys 3 items, a discount of 16% is given on the total marked price.\nRadha buys 5 items in one purchase.\nWhat is the overall effective discount percentage on her purchase?

Introduction / Context:
This question tests the understanding of tiered discount structures. Instead of a single discount rate for any quantity, different discounts apply depending on whether the customer buys 2 items or 3 items. When a customer buys 5 items, we need to decide how to split the purchase across the available discount slabs to compute the total effective discount.

Given Data / Assumptions:

• Marked price of each item = Rs. 500.
• For buying 2 items together, the discount is 8% on the combined marked price.
• For buying 3 items together, the discount is 16% on the combined marked price.
• Radha buys a total of 5 items in one purchase.
• We assume the best possible use of slabs: 2 items get 8% discount and 3 items get 16% discount.

Concept / Approach:
We first compute the total amount Radha would pay with no discount. Then we calculate the discounted cost for the group of 2 items and the group of 3 items separately, using their respective discount rates. Adding these gives the actual amount paid. Finally, the effective discount percentage is obtained by comparing the total marked price with this actual payment, using the formula effective discount = (marked total - paid total) / marked total * 100.

Step-by-Step Solution:
Step 1: Total marked price with no discount = 5 items * Rs. 500 each = Rs. 2,500.Step 2: For the 2 item slab, combined marked price = 2 * 500 = Rs. 1,000.Step 3: Discount on 2 items = 8% of 1,000 = 1,000 * 8 / 100 = Rs. 80, so Radha pays 1,000 - 80 = Rs. 920 for these 2 items.Step 4: For the 3 item slab, combined marked price = 3 * 500 = Rs. 1,500.Step 5: Discount on 3 items = 16% of 1,500 = 1,500 * 16 / 100 = Rs. 240, so Radha pays 1,500 - 240 = Rs. 1,260 for these 3 items.Step 6: Total amount actually paid = 920 + 1,260 = Rs. 2,180.Step 7: Total discount received = original total 2,500 - actual payment 2,180 = Rs. 320.Step 8: Effective discount percentage = (320 / 2,500) * 100 = 12.8 percent.

Verification / Alternative check:
We can also compute the average discount per item. Total discount is Rs. 320 on 5 items, so discount per item is 320 / 5 = Rs. 64. As a percentage of 500, that is (64 / 500) * 100 = 12.8 percent. This matches the earlier calculation and confirms that the overall effective discount is 12.8 percent.

Why Other Options Are Wrong:
20.4 percent and 23.25 percent would both require a larger discount amount than Rs. 320; they do not match the computed figures for slab wise discounts.
12.8 percent is exactly what we derived, so this is the correct choice.
35 percent would correspond to a huge discount of 875 rupees, which is much more than the sum of the slab wise discounts.
16 percent is simply the discount rate for 3 items, not the combined effective rate across 5 items with mixed slabs.

Common Pitfalls:
A common mistake is to average the two discount percentages (8% and 16%) or to apply 16% on all 5 items, which ignores the slab structure. Another mistake is to forget that discounts apply on the combined marked price for each slab, not on the total original bill directly. To avoid errors, always split the purchase into the defined slabs, compute each part separately, sum the actual payments, and then derive the effective discount from the grand total.

Final Answer:
Radha receives an overall effective discount of 12.8 percent on her purchase of 5 items.