A Rs 1000 box of cookies is offered at 10% discount and a Rs 400 bar of chocolate is offered at 8% discount. If a customer buys 2 boxes of cookies and 3 bars of chocolate in one purchase, what is the overall effective discount percentage on the total marked price of all items?

Introduction / Context:
This question tests the concept of effective discount when multiple items with different discount rates are bought together. Instead of looking at each discount separately, we must compare the total amount saved with the total marked price to find a single equivalent discount percentage on the whole purchase.

Given Data / Assumptions:

• Marked price of one box of cookies = Rs 1000
• Marked price of one bar of chocolate = Rs 400
• Discount on cookies = 10 percent
• Discount on chocolates = 8 percent
• Number of cookie boxes bought = 2
• Number of chocolate bars bought = 3
• We assume there are no extra taxes or additional discounts beyond those mentioned.

Concept / Approach:
The effective discount is calculated by first finding:

• Total marked price of all items without discount
• Total amount actually paid after applying individual discounts
• Total savings = Total marked price - Total selling price

Then, Effective discount percent = (Total savings / Total marked price) * 100.

Step-by-Step Solution:
Step 1: Total marked price of cookies = 2 * 1000 = Rs 2000. Step 2: Total marked price of chocolates = 3 * 400 = Rs 1200. Step 3: Combined total marked price = 2000 + 1200 = Rs 3200. Step 4: Selling price of one cookie box after 10 percent discount = 1000 * (1 - 10/100) = 1000 * 0.90 = Rs 900. Step 5: Selling price for 2 boxes of cookies = 2 * 900 = Rs 1800. Step 6: Selling price of one chocolate bar after 8 percent discount = 400 * (1 - 8/100) = 400 * 0.92 = Rs 368. Step 7: Selling price for 3 bars of chocolate = 3 * 368 = Rs 1104. Step 8: Total selling price = 1800 + 1104 = Rs 2904. Step 9: Total savings = Total marked price - Total selling price = 3200 - 2904 = Rs 296. Step 10: Effective discount percent = (296 / 3200) * 100 = 9.25 percent.

Verification / Alternative check:
We can also compute the effective discount by first finding the average discount per rupee. The total discount is Rs 296 on a base of Rs 3200. This ratio is 296 / 3200 = 0.0925, which corresponds to 9.25 percent. This confirms our earlier calculation, so the result is consistent.

Why Other Options Are Wrong:
9 percent: This underestimates the savings because it assumes a slightly smaller total discount than actually received.
8.75 percent: This also underestimates the effective discount and does not match the exact ratio of savings to marked price.
8.5 percent: This is even further from the correct value and ignores the precise calculation of selling prices.
9.5 percent: This overestimates the discount and would imply more savings than are actually obtained from the given offers.

Common Pitfalls:
Students often try to average the discount rates directly, for example by taking the simple average of 10 percent and 8 percent. That method is incorrect because the items have different prices and quantities, so each part contributes differently to the total. Another common mistake is to ignore the total marked price and compute discount only on one item type. Always base the effective discount on the complete bill, not on individual products separately.

Final Answer:
The overall effective discount on the combined purchase of cookies and chocolates is 9.25 percent.