To solve the given problem, let's assume the cost price (C.P.) of the article is Rs. x.
Step 1: Understand the percentage profit and loss
The percentage profit earned by selling the article for Rs. 1920 is equal to the percentage loss incurred by selling the article for Rs. 1280.
When selling for Rs. 1920, the profit percentage is: Profit = 1920 - x Profit Percentage = [(1920 - x) / x] * 100
When selling for Rs. 1280, the loss percentage is: Loss = x - 1280 Loss Percentage = [(x - 1280) / x] * 100
According to the problem, these two percentages are equal: [(1920 - x) / x] * 100 = [(x - 1280) / x] * 100
Step 2: Simplify the equation
By cancelling out the common factor of 100 and solving the equation: (1920 - x) / x = (x - 1280) / x
Cross-multiply to eliminate the denominators: (1920 - x) = (x - 1280)
Now solve for x: 1920 - x = x - 1280 1920 + 1280 = 2x 3200 = 2x x = 1600
Step 3: Calculate the selling price for a 25% profit
Now that we know the cost price (C.P.) is Rs. 1600, we need to find the selling price (S.P.) for a 25% profit.
The formula for selling price with profit is: S.P. = C.P. + (Profit Percentage * C.P.)
S.P. = 1600 + (25% of 1600) S.P. = 1600 + (0.25 * 1600) S.P. = 1600 + 400 S.P. = 2000
Final Answer:
The article should be sold for Rs. 2000 to make a 25% profit.
The correct option is (a) Rs. 2000.
