If a saree is sold for Rs 2880, the seller incurs a loss of 10%. At what price (in rupees) should the saree be sold instead in order to earn a profit of 20%?

Introduction / Context:
This is a straightforward profit and loss question where we move from a known loss situation to a desired profit situation on the same item. The main idea is to first recover the cost price using the loss information and then use that cost price to find the selling price corresponding to the desired profit percentage.

Given Data / Assumptions:

• Selling price with loss is Rs 2880.
• At this price the seller faces a loss of 10%.
• The same saree is to be sold to earn a profit of 20%.
• Cost price of the saree remains constant.

Concept / Approach:
When there is a loss of 10%, selling price is 90% of cost price. Using SP = CP * (1 - loss_percent / 100), we can determine cost price. After that, to achieve a 20% profit, we use SP = CP * (1 + profit_percent / 100). This two step process, first backward to CP and then forward to new SP, is very typical for such questions.

Step-by-Step Solution:
Let the cost price of the saree be CP.Given loss is 10%, so SP1 = CP * (1 - 10 / 100) = 0.90 * CP.But SP1 is Rs 2880, so 0.90 * CP = 2880.Therefore CP = 2880 / 0.90 = Rs 3200.Now we want a profit of 20%, so SP2 = CP * (1 + 20 / 100) = 1.20 * CP.SP2 = 1.20 * 3200 = Rs 3840.

Verification / Alternative check:
Check with the cost price: at CP = Rs 3200, a 10% loss means selling at 90% of CP which is 0.90 * 3200 = Rs 2880, matching the given loss situation. For 20% profit, 1.20 * 3200 = Rs 3840, which is consistent and confirms our answer.

Why Other Options Are Wrong:
Values like 3480 or 4380 correspond to different profit percentages when compared to the cost price of Rs 3200. For example, 3480 would give only 8.75% profit and 4380 would give about 36.875% profit. 4830 is much higher and would lead to an even larger profit. Only Rs 3840 yields exactly 20% profit.

Common Pitfalls:
Sometimes students directly adjust the old selling price by adding 30% (10% loss to 20% profit) on 2880, which is incorrect because profit and loss are always calculated on cost price, not on the previous selling price. Always go back to cost price first and then move forward to a new selling price based on the required profit percentage.

Final Answer:
The saree should be sold for Rs 3840 to earn a 20% profit.