A bread seller X marks the price of each bread packet 150% above its cost price and usually allows a discount of 40% on the marked price, making a profit of Rs. 30 on each packet. If instead X allows a discount of 37.5% on the marked price, what total profit will he earn by selling 80 bread packets?

Introduction / Context:
This problem combines markup, discount, and absolute profit per unit in a single scenario. First, the bread seller marks his goods 150% above cost, then offers various discount percentages on this marked price. The question asks for the resulting total profit when the discount rate is changed but the cost price and marked price structure remain the same. Such questions are typical in profit and loss topics and test the ability to move between absolute rupee profit and percentage-based pricing strategies in a clear, stepwise manner.

Given Data / Assumptions:
- Let cost price per bread packet be C rupees. - Marked price (MP) is 150% above cost price, so MP = C * (1 + 1.5) = 2.5C. - With a 40% discount on MP, profit per packet is Rs. 30. - Later, discount is changed to 37.5% on MP. - We must find the total profit on 80 packets at the 37.5% discount rate.

Concept / Approach:
First we use the initial situation (40% discount, Rs. 30 profit) to determine the actual cost price C and marked price MP. Under a 40% discount, the selling price SP1 is 60% of MP (because 100% - 40% = 60%). The profit per packet in this situation is SP1 - C, which is given as Rs. 30. This gives us an equation in terms of C that we can solve. Once we know C and MP, we consider the second scenario with a 37.5% discount, compute the new selling price per packet, find the new profit per packet, and then multiply by 80 packets to get total profit.

Step-by-Step Solution:
Marked price MP = 2.5C (since markup is 150% on cost). With a 40% discount, selling price SP1 = 60% of MP = 0.60 * 2.5C = 1.5C. Profit per packet in this case = SP1 - C = 1.5C - C = 0.5C. Given that this profit is Rs. 30, we have 0.5C = 30. So, C = 30 / 0.5 = 60 rupees. Therefore, MP = 2.5 * 60 = Rs. 150. Now consider the discount of 37.5%: new selling price SP2 = (100% - 37.5%) of MP = 62.5% of MP. So, SP2 = 0.625 * 150 = Rs. 93.75. New profit per packet = SP2 - C = 93.75 - 60 = Rs. 33.75. For 80 packets, total profit = 33.75 * 80 = Rs. 2,700.

Verification / Alternative check:
Recheck cost price and first scenario: MP = Rs. 150, 40% discount gives SP1 = 90, which would be a profit of 30 over C = 60. This matches the given condition. Recheck second scenario: 37.5% of 150 is 56.25, so discount amount = 56.25 and SP2 = 150 - 56.25 = 93.75. Profit per packet is 93.75 - 60 = 33.75, and 33.75 * 80 = 2,700, verifying our answer.

Why Other Options Are Wrong:
- Rs. 2,500 and Rs. 2,750 assume incorrect values for either cost price or new profit per packet. - Rs. 3,000 and Rs. 3,200 are too high and do not match the computed profit per packet. - Only Rs. 2,700 is consistent with both the given initial profit and the new discount rate.

Common Pitfalls:
Some students mistakenly apply the discount directly on cost price instead of marked price, which leads to a wrong value of cost price. Another frequent mistake is to add or subtract percentage values incorrectly instead of calculating actual rupee amounts for each step. Rounding off intermediate values too early, especially with decimals like 93.75, can create slight errors in the final profit figure.

Final Answer:
When offering a 37.5% discount, X earns a total profit of Rs. 2,700 on 80 bread packets.