A stall sells a pizza for Rs 200 and incurs a loss of 20%. At what price (in rupees) should the stall sell the same pizza in order to make a profit of 10%?

Introduction / Context:
This is a straightforward profit and loss calculation involving two different selling situations for the same item. The stall first sells at a known loss percentage and we are asked to adjust the price so that a target profit percentage is achieved on the same cost price. This tests your ability to reverse engineer the cost price from a loss scenario and then compute a new selling price for a desired profit.

Given Data / Assumptions:

• Pizza sold at Rs 200 gives a loss of 20%.
• Let cost price of the pizza be C.
• We want a selling price that yields a profit of 10% on the same cost price.
• We need this new selling price in rupees.

Concept / Approach:
We use:

• Loss of 20% means SP = 80% of CP, or SP = 0.8C.
• Given SP = 200, solve for C.
• Then for a profit of 10%, new SP = 110% of C, or SP = 1.1C.
• Calculate 1.1C with the cost price obtained.

Step-by-Step Solution:
Let cost price of the pizza be C. Loss of 20% means SP1 = 0.8C. Given SP1 = 200, so 0.8C = 200. C = 200 / 0.8. C = 250. For a profit of 10%, new selling price SP2 = 1.1C. SP2 = 1.1 * 250. SP2 = 275. Thus, the pizza must be sold for Rs 275 to earn a 10% profit.

Verification / Alternative check:
Check quickly with the cost price:

• Cost price C = 250.
• At SP = 200, loss = 250 - 200 = 50, loss percent = (50 / 250) * 100 = 20%.
• At SP = 275, profit = 275 - 250 = 25, profit percent = (25 / 250) * 100 = 10%.

Both calculations are consistent with the conditions in the question, so our answer is correct.

Why Other Options Are Wrong:
Selling at 250 would only cover cost price with no profit or loss. Selling at 300 would give a profit of 20%, not 10%. Selling at 325 gives an even higher profit. Selling at 260 gives profit of only (260 - 250) / 250 * 100 = 4%, which is not equal to 10%. Therefore only Rs 275 gives exactly 10% profit.

Common Pitfalls:
Students sometimes treat the 20% loss incorrectly as 20% of selling price instead of cost price. Another error is to add 10% directly on the earlier selling price rather than the cost price. Always compute or infer the cost price first and then apply the desired profit percentage on that cost price to find the correct new selling price.

Final Answer:
The stall should sell the pizza for Rs 275 to make a 10% profit.