Namitha sells a power bank for Rs 1,950 at a loss of 25% on its cost price. At what price should she sell the same power bank to earn a profit of 25% on the cost price?

Introduction / Context:
This is a classic cost price and selling price conversion question where the article is first sold at a loss and later is to be sold at a profit. You are given one selling price and the loss percentage, and you must then calculate another selling price for a desired profit percentage. Such questions test your ability to move between different percentage conditions using the same cost price.

Given Data / Assumptions:

• Current selling price SP₁ = Rs 1,950.
• Loss at SP₁ = 25% of cost price.
• The same power bank should now be sold at a profit of 25% on the cost price.
• We assume cost price of the article does not change.
• We need to find the new selling price SP₂.

Concept / Approach:
If an item is sold at a loss of L%, then SP = (1 - L%) * CP. Similarly, for a profit of P%, SP = (1 + P%) * CP. So we first find the cost price from the loss case, and then use it to compute the selling price for the desired profit. This two-step method is straightforward and avoids confusion between loss and profit conditions.

Step-by-Step Solution:
Step 1: Let cost price = CP.Step 2: A loss of 25% implies SP₁ = 0.75 * CP.Step 3: Given SP₁ = 1,950, so 1,950 = 0.75 * CP ⇒ CP = 1,950 / 0.75 = 2,600.Step 4: To gain 25%, new SP₂ must be 1.25 * CP = 1.25 * 2,600 = 3,250.Step 5: Therefore, the required selling price is Rs 3,250.

Verification / Alternative check:
Check the calculations from cost price. Selling at 1,950 means loss = 2,600 - 1,950 = 650, and loss% = (650 / 2,600) * 100 = 25%, which matches the given data. Selling at 3,250 gives profit = 3,250 - 2,600 = 650, and profit% = (650 / 2,600) * 100 = 25%. Both conditions are satisfied, confirming that our cost price and new selling price are correct.

Why Other Options Are Wrong:
Values like Rs 3,680, Rs 3,560 and Rs 3,320 correspond to much higher or lower profit percentages when compared to the cost price of Rs 2,600. They do not give exactly 25% profit, so they cannot be correct. They are included as plausible looking numbers to test whether you have applied the formulas correctly.

Common Pitfalls:
Learners sometimes assume that the difference between the loss selling price and the profit selling price must be a fixed amount like Rs 1,300 or try to apply percentages directly on the selling prices rather than cost price. Always remember that both loss% and profit% are calculated on cost price. Mixing bases leads to wrong answers in percentage questions.

Final Answer:
Namitha must sell the power bank for Rs. 3250 to earn a 25% profit on the cost price.