Profit Calculation for Selling Articles: A Detailed Analysis
Here is a detailed analysis on how to determine the profit percentage at which to sell the remaining one-third of articles to achieve an overall profit of 13%. This problem requires breaking down the process into several steps, each focusing on the given data and calculations involved.
Determine the Cost Price (CP) of the Articles
The total cost price (CP) of the articles is given as Rs. 5400.
Step 1: Determine the cost price of 2?3 of the articles.
C
Step 2: Calculate the selling price (SP) for this portion at a 5% profit.
SP2/3 CP2/3 5% of CP2/3 3600 0.05 × 3600 3600 180 3780.
Calculate the Overall Selling Price (SP) for an Overall Profit of 13%
To achieve an overall 13% profit, the selling price must be:
SPoverall CP 13% of CP 5400 0.13 × 5400 5400 702 6102.
Calculate the Selling Price (SP) of the Remaining One-Third of the Articles
The selling price of the remaining one-third of the articles can be calculated by subtracting the selling price of the 2/3 portion from the overall selling price.
SP1/3 SPoverall - SP2/3 6102 - 3780 2322.
Step 3: Determine the cost price of the remaining one-third of the articles.
CP1/3 1?3 × 5400 1800.
Calculate the Profit Percentage for the Remaining One-Third of the Articles
The profit made on this portion is:
Profit SP1/3 - CP1/3 2322 - 1800 522.
The profit percentage is calculated as:
Profit Percent (Profit / CP1/3) × 100 (522 / 1800) × 100 ≈ 29.
Thus, the profit percentage at which he sold the remaining one-third of the articles is approximately 29%.
Purchase and Sale Analysis
Purchase amount of articles Rs 5400
Total sale amount of the articles to gain 13 over all 5400 × 113/100 Rs 6102
Sale amount of 2/3 of the articles at 5% profit 5400 × 2/3 × 105/100 Rs 3780
Sale amount to be realised on remaining 1/3 of articles 6102 – 3780 Rs 2322
Conclusion
This breakdown and step-by-step analysis provide a clear understanding of how to calculate the profit percentage and overall selling price for achieving a desired profit margin in a business transaction involving multiple sales stages.