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 bucket contains liquid A and B in the ratio 17:18. 140 litre of the mixture is taken out and filled with 140 litre of B. Now the ratio changes to 7:8. Find the quantity of liquid B initially. (In litres)
- A trader mixes 245 kg of rice at Rs. 155 per kg with 255 kg of rice of other variety at Rs. 155 per kg and sells the mixture at Rs.186 per kg. Find his profit percent.
- A trader mixes 255 kg of rice at Rs.170 per kg with 265 kg of rice of other variety at Rs. 170 per kg and sells the mixture at Rs.204 per kg. Find his profit percent.
5 litres are drawn from a cask full of wine and is then filled with water. This operation is performed once more. The ratio of the quantity of wine now left in cask to that of the water is 16:9. How much wine the cask hold originally? (In litres)
- In what ratio must a grocer mix two varieties of pulses costing Rs.66 and Rs.88 per kg respectively so as to get a mixture worth Rs.76 per kg?
