A person incurs a loss of 5% by selling a watch for Rs. 1140. At what price should the watch be sold to earn a profit of 5% on the cost price?

Introduction / Context:
This question moves from a loss situation to a desired profit on the same item. It requires first recovering the cost price from a given selling price and loss percentage, and then computing a new selling price that yields a specified profit percentage. This type is frequent in basic profit and loss practice.

Given Data / Assumptions:

• The watch is sold at Rs. 1140 with a loss of 5%.
• The cost price remains the same for both transactions.
• We want a 5% profit on the cost price in the new sale.
• We must find the required selling price for 5% profit.

Concept / Approach:
A loss of 5% means the selling price is 95% of the cost price. From SP = 1140 we can compute CP as 1140 divided by 0.95. Once CP is known, a profit of 5% implies a new selling price equal to 105% of CP. Working systematically with percentages as decimals makes the computation straightforward.

Step-by-Step Solution:
Step 1: Let CP be the cost price of the watch.Step 2: Loss of 5% implies selling price SP1 = 0.95 * CP.Step 3: Given SP1 = Rs. 1140, so 0.95 * CP = 1140.Step 4: Therefore CP = 1140 / 0.95.Step 5: Calculate CP: 0.95 = 95 / 100, so CP = 1140 * 100 / 95 = 114000 / 95 = Rs. 1200.Step 6: To earn a 5% profit, required selling price SP2 = 1.05 * CP = 1.05 * 1200 = Rs. 1260.

Verification / Alternative check:
Check the loss case: selling at Rs. 1140 when CP = Rs. 1200 gives loss = 60, and loss percentage = 60 / 1200 * 100 = 5%.Check the profit case: selling at Rs. 1260 gives profit = 1260 - 1200 = 60, and profit percentage = 60 / 1200 * 100 = 5%.Thus both conditions are satisfied with CP = 1200 and SP2 = 1260.

Why Other Options Are Wrong:
Rs. 1200 corresponds to selling at cost price, giving zero profit. Rs. 1230 would be a profit of 30 on a cost of 1200, which is only 2.5%. Rs. 1290 gives a profit of 90, or 7.5%, and Rs. 1320 gives a profit of 120, or 10%. Only Rs. 1260 yields exactly a 5% profit.

Common Pitfalls:
Some learners mistakenly subtract 5 rupees instead of 5% or mix up the direction of the percentage, treating 1140 as 105% of cost instead of 95%. Others attempt to find the difference between loss and profit percentages directly without recovering the cost price. Always anchor all calculations on the cost price when dealing with profit and loss percentages.

Final Answer:
The watch should be sold for Rs. 1260 to earn a 5% profit.