The percentage profit earned by James by selling an article for 1,920 equals the percentage loss suffered by selling it at 1,500. What should be the selling price if he wants to earn a 10% profit?

Explanation

Step 1: Set Up the Problem Let CPCPCP be the cost price of the article. When James sells the article for 1,9201,9201,920, he makes a profit. The profit percentage can be expressed as: 1. Profit=SP1−CP=1920−CP\text{Profit} = SP_1 - CP = 1920 - CPProfit=SP1​ −CP=1920−CP Profit Percentage=(1920−CPCP)×100\text{Profit Percentage} = \left(\frac{1920 - CP}{CP}\right) \times 100Profit Percentage=(CP1920−CP​ )×100 When James sells the article for 1,5001,5001,500, he incurs a loss. The loss percentage can be expressed as: 1. Loss=CP−SP2=CP−1500\text{Loss} = CP - SP_2 = CP - 1500Loss=CP−SP2​ =CP−1500 Loss Percentage=(CP−1500CP)×100\text{Loss Percentage} = \left(\frac{CP - 1500}{CP}\right) \times 100Loss Percentage=(CPCP−1500​ )×100 Step 2: Equate the Profit Percentage and Loss Percentage According to the problem, the percentage profit earned by selling at 1,9201,9201,920 equals the percentage loss suffered by selling at 1,5001,5001,500: 1920−CPCP×100=CP−1500CP×100\frac{1920 - CP}{CP} \times 100 = \frac{CP - 1500} {CP} \times 100CP1920−CP​×100=CPCP−1500​×100 Step 3: Simplify the Equation We can cancel out 100100100 from both sides: 1920−CPCP=CP−1500CP\frac{1920 - CP}{CP} = \frac{CP - 1500}{CP}CP1920−CP​ =CPCP−1500​ Cross-multiplying gives: 1920−CP=CP−15001920 - CP = CP - 15001920−CP=CP−1500 Rearranging terms leads to: 1920+1500=2CP1920 + 1500 = 2CP1920+1500=2CP CP=34202=1710CP = \frac{3420} {2} = 1710CP=23420​=1710 Step 4: Calculate the Selling Price for a 10% Profit To find the selling price for a 10% profit: Selling Price=CP+Profit\text{Selling Price} = CP + \text{Profit}Selling Price=CP+Profit Where profit is: Profit=10% of CP=10100×1710=171\text{Profit} = 10\% \text{ of } CP = \frac{10}{100} \times 1710 = 171Profit=10% of CP=10010​×1710=171 Thus, the selling price should be: Selling Price=1710+171=1881\text{Selling Price} = 1710 + 171 = 1881Selling Price=1710+171=1881 Answer: The selling price if he wants to earn a 10% profit should be Rs 1,881.