The marked price of an item is Rs. 400. The discount is 6% on buying 1 item and 24% on buying 4 items. Rachita buys 5 items in total. What is the effective discount percentage on her total bill?

Introduction / Context:
This question tests understanding of effective discount when different units of the same item are sold at different discount rates. Rachita buys some items with a small discount and some items with a larger discount. We are asked to find one overall discount percentage on the entire marked price value of all items combined. This is similar to calculating a weighted average of discounts based on the marked price contribution of each group of items.

Given Data / Assumptions:
Marked price (MP) per item = Rs. 400.
Discount on buying 1 item = 6 percent.
Discount on buying 4 items together = 24 percent.
Rachita buys 1 item at 6 percent discount and 4 items at 24 percent discount, total 5 items.
We must find the effective discount percentage on the total marked price of 5 items.

Concept / Approach:
We first compute the total marked price for all 5 items, then compute the total amount actually paid after applying the different discounts to the respective groups. The difference between total marked price and total paid amount gives the total discount in rupees. The effective discount percentage is then (total discount / total marked price) * 100. This is effectively a weighted average discount with weights equal to the marked price contributions of each group of items.

Step-by-Step Solution:
Marked price per item = Rs. 400. Total items bought by Rachita = 5. Total marked price for 5 items = 5 * 400 = 2000. She buys 1 item at 6 percent discount. Marked price for that 1 item = 400, discount = 6 percent of 400 = 0.06 * 400 = 24, so she pays 400 - 24 = 376. She buys 4 items at 24 percent discount. Marked price for 4 items = 4 * 400 = 1600, discount = 24 percent of 1600 = 0.24 * 1600 = 384, so she pays 1600 - 384 = 1216. Total amount paid = 376 + 1216 = 1592. Total discount in rupees = total marked price - total amount paid = 2000 - 1592 = 408. Effective discount percentage = (408 / 2000) * 100 = 20.4 percent.

Verification / Alternative check:
We can also think of the effective discount as the ratio of total discount to total marked price. Since the calculations above give 408 as total discount and 2000 as total marked price, the fraction is 0.204. Converting to percentage gives 0.204 * 100 = 20.4 percent. This matches our direct computation, confirming internal consistency. Any other effective discount value would not match the computed payment of Rs. 1592.

Why Other Options Are Wrong:
An effective discount of 34 percent would mean she pays only 66 percent of 2000, that is 1320, which is less than the 1592 she actually pays. A discount of 12.8 percent would imply a total discount of 256, not 408. A discount of 23.25 percent would give a total discount of 465, which is larger than the calculated discount. Only 20.4 percent matches the actual total discount she receives on the combined purchase.

Common Pitfalls:
Many students incorrectly average the two discount percentages directly (for example, (6 percent + 24 percent) / 2), ignoring the fact that the number of items and total marked value are different for each discount. Others mistakenly average based on the count of items without considering the same marked price per item, which in this case would give the same result for counts but is conceptually confusing. The safe method is always to work in rupees: compute total marked price, compute total amount paid with actual discounts, and then calculate the effective discount from the overall difference.

Final Answer:
The effective discount on Rachita's total purchase is 20.4 percent.