The discount offered on a shirt with marked price 500 rupees is 20 percent, and the discount on a pair of trousers with marked price 1,000 rupees is 40 percent. If Ajay buys 2 shirts and 3 pairs of trousers, what is the effective overall discount percentage on his total purchase?

Introduction / Context:
This is a mixed discount problem where different items have different discount rates. The goal is to find the effective discount percentage on the total bill. Such questions mimic real shopping situations and require careful calculation of total marked price and total amount paid before computing the single equivalent discount percentage.

Given Data / Assumptions:
- Marked price of one shirt = 500 rupees, discount on shirts = 20 percent.
- Marked price of one pair of trousers = 1,000 rupees, discount on trousers = 40 percent.
- Ajay buys 2 shirts and 3 pairs of trousers.
- We must find the overall effective discount percentage on the combined purchase.

Concept / Approach:
First calculate the total marked price of all items. Then apply the respective discounts to each category to get the actual amount paid. The difference between total marked price and total amount paid gives the total discount. Finally, the effective discount percentage is total discount divided by total marked price, times 100.

Step-by-Step Solution:
Step 1: Total marked price of shirts = 2 * 500 = 1,000 rupees.Step 2: Total marked price of trousers = 3 * 1,000 = 3,000 rupees.Step 3: Overall marked price = 1,000 + 3,000 = 4,000 rupees.Step 4: Discount on shirts = 20 percent of 1,000 = 0.20 * 1,000 = 200 rupees; so Ajay pays 800 rupees for shirts.Step 5: Discount on trousers = 40 percent of 3,000 = 0.40 * 3,000 = 1,200 rupees; so Ajay pays 1,800 rupees for trousers.Step 6: Total amount paid = 800 + 1,800 = 2,600 rupees.Step 7: Total discount = Total marked price - Total amount paid = 4,000 - 2,600 = 1,400 rupees.Step 8: Effective discount percentage = (1,400 / 4,000) * 100 = 35 percent.

Verification / Alternative check:
You can also think in terms of weighted average discount rates. Shirts contribute 1,000 out of 4,000 of the marked price and have 20 percent discount; trousers contribute 3,000 out of 4,000 and have 40 percent discount. Weighted discount = (1,000 / 4,000) * 20 + (3,000 / 4,000) * 40 = 0.25 * 20 + 0.75 * 40 = 5 + 30 = 35 percent. This matches the earlier calculation.

Why Other Options Are Wrong:
- 30 percent and 32 percent underestimate the savings and do not match the actual discount amount of 1,400 rupees.
- 25 percent is far too low and would correspond to a discount of only 1,000 rupees on 4,000 rupees of goods.

Common Pitfalls:
Some students mistakenly average the two discount percentages directly, for example (20 percent + 40 percent) / 2 = 30 percent, without considering that the total marked price spent on each category is different. The correct approach is to use actual rupee values or a weighted average based on total marked price contributions. Always compute total marked price, total amount paid, and then derive the effective percentage from these totals.

Final Answer:
The effective overall discount percentage Ajay receives is 35 percent.