A Profit-Maximizing Approach to Selling Mixed Rice: A Practical Guide

Understanding the principle of profit maximization is crucial for any business dealing with goods such as rice. In this article, we will delve into a practical scenario where a man named Mr. X purchased two different qualities of rice and then sold them at a profit. This guide will walk you through the steps and calculations involved in determining the selling price per kilogram of mixed rice.

Investigating Mr. X's Rice Purchase and Sale

Mr. X made two separate purchases of rice: 45 kg at Rs. 28 per kg and 25 kg at Rs. 32 per kg. To determine the optimal selling price that would yield a 40% profit, we need to perform a series of calculations.

Step 1: Calculate the Total Cost of Rice

The cost of the first batch of rice can be calculated as:

Cost_1 45 kg × 28 Rs/kg 1260 Rs

The cost of the second batch of rice is calculated similarly:

Cost_2 25 kg × 32 Rs/kg 800 Rs

Adding these two costs together gives the total cost of the rice purchased:

Total Cost Cost_1 Cost_2 1260 Rs 800 Rs 2060 Rs

Step 2: Calculate the Total Quantity of Rice

The total quantity of rice can be found by adding the quantities of the two batches:

Total Quantity 45 kg 25 kg 70 kg

Step 3: Calculate the Selling Price for a 40% Profit

To achieve a 40% profit, we first calculate the profit as a percentage of the total cost:

Profit 40% of Total Cost 0.40 × 2060 Rs 824 Rs

The total selling price is then the sum of the total cost and the profit:

Total Selling Price Total Cost Profit 2060 Rs 824 Rs 2884 Rs

Step 4: Calculate the Selling Price Per Kg

The final step is to determine the selling price per kilogram of the mixed rice:

Selling Price per kg Total Selling Price / Total Quantity 2884 Rs / 70 kg ≈ 41.20 Rs/kg

Thus, Mr. X should sell the mixed rice at approximately Rs 41.20 per kilogram.

Alternative Method: A Simplified Approach

An alternative method to solve this problem involves calculating the cost per kilogram of the mixed rice and then adding the desired profit to find the selling price per kilogram.

Method 2: Cost Price Calculation

The cost price of the first batch of rice is:

Total Purchase Cost 1260 Rs

The cost price of the second batch of rice is:

Total Purchase Cost 800 Rs

The total purchase cost for 70 kg of rice is:

Total Purchase Cost 1260 Rs 800 Rs 2060 Rs

The cost price per kilogram is:

Cost Price per kg Total Purchase Cost / Total Quantity 2060 Rs / 70 kg ≈ 29.43 Rs

To achieve a 40% profit, we add 40% of the cost price per kilogram to the cost price per kilogram:

Selling Price per kg Cost Price per kg 40% of Cost Price per kg

29.43 Rs 11.77 Rs 41.20 Rs

Thus, the selling price per kilogram of the mixed rice is approximately Rs 41.20.

Conclusion

By carefully calculating the cost and determining the desired profit margin, Mr. X can sell his mixed rice at an optimal price to maximize his profits. The calculations show that he should sell the mixed rice at approximately Rs 41.20 per kg to achieve a 40% profit.

Understanding these principles can help businesses in various industries, including agriculture, to make informed decisions when selling goods. Whether you are a rice trader, a grocery store owner, or a farmer, the knowledge of cost calculation and profit maximization is invaluable.