At what price per kg should he sell the mixed variety of wheat to earn 10% profit?
Calculating Wheat Selling Price for 10% Profit
The problem requires finding the selling price per kg for a mixture of wheat to achieve a specific profit margin.
Cost Price Calculation
- Cost of first lot of wheat: The shopkeeper bought 10 kg at ₹20 per kg.
Cost1 = 10 \text{ kg} \times ₹20/\text{kg} = ₹200
- Cost of second lot of wheat: The shopkeeper bought 15 kg at ₹30 per kg.
Cost2 = 15 \text{ kg} \times ₹30/\text{kg} = ₹450
- Total Cost Price (CP): Sum of the costs of both lots.
Total CP = Cost1 + Cost2 = ₹200 + ₹450 = ₹650
- Total Quantity of Wheat: Sum of the quantities from both lots.
Total Quantity = 10 \text{ kg} + 15 \text{ kg} = 25 \text{ kg}
Average Cost Price Per Kg
Calculate the average cost price per kilogram for the mixed wheat.
Average CP per kg = \frac{\text{Total Cost Price}}{\text{Total Quantity}}
Average CP per kg = \frac{₹650}{25 \text{ kg}} = ₹26/\text{kg}
Profit Calculation
The shopkeeper wants to earn a 10% profit on the cost price.
- Profit Amount per kg: Calculate 10% of the average CP per kg.
\text{Profit per kg} = 10\% \times ₹26/\text{kg} = 0.10 \times ₹26/\text{kg} = ₹2.60/\text{kg}
Selling Price Calculation
The selling price (SP) per kg is the average cost price plus the desired profit per kg.
SP per kg = Average CP per kg + Profit per kg
SP per kg = ₹26/\text{kg} + ₹2.60/\text{kg}
SP per kg = ₹28.60/\text{kg}
Therefore, the shopkeeper should sell the mixed variety of wheat at ₹28.60 per kg to earn a 10% profit.
Important Questions from Mixture Problems
A mixture of acid and water contains 20 percent acid. When 10 litres of water is added to the mixture, then the percentage of acid becomes 15 percent. What is the original quantity of mixture ?
A container contains 20 L mixture in which there is 10% sulphuric acid. Find the quantity of sulphuric acid to be added in it to make the solution to contain 25% sulphuric acid.
The ratio of milk to water in a 100 litres mixture is 2 ∶ 3. 10 litres of this mixture is withdrawn and replaced with milk. This process is repeated 2 more times, What is the percentage of milk in final mixture ?
- 80% and 90% pure acid solutions are mixed to obtain 20 litres of 87% pure acid solution. Find the quantity (in litres) of 80% pure acid solution taken to form the mixture.
Some fruits are bought at a rate of 11 for Rs. 100 and an equal number at a rate of 9 for Rs. 100. If all the fruits are sold at a rate of 10 for Rs. 100, then what is the gain or loss percent in the entire transaction?
