1. **Problem Statement:** A trader buys 50 kg of type q groundnuts at 130 per kg and 75 kg of type r groundnuts at 180 per kg, then mixes them. 2. **(a)(i) Find the cost price per kg of the mixture:** - Total cost of type q = $50 \times 130 = 6500$ - Total cost of type r = $75 \times 180 = 13500$ - Total weight = $50 + 75 = 125$ kg - Total cost = $6500 + 13500 = 20000$ - Cost price per kg of mixture = $\frac{20000}{125} = 160$ 3. **(a)(ii) Calculate percentage profit when 80% sold at 170 and 20% at 180:** - Total mixture weight = 125 kg - Weight sold at 170 = $0.8 \times 125 = 100$ kg - Weight sold at 180 = $0.2 \times 125 = 25$ kg - Revenue from 170/kg = $100 \times 170 = 17000$ - Revenue from 180/kg = $25 \times 180 = 4500$ - Total revenue = $17000 + 4500 = 21500$ - Cost price = $20000$ - Profit = $21500 - 20000 = 1500$ - Percentage profit = $\frac{1500}{20000} \times 100 = 7.5\%$ 4. **(b) Find the ratio of mixing for 25% profit when selling at 200 per kg:** - Let the ratio of type q to type r be $x : y$ - Cost price per kg of mixture = $C = \frac{130x + 180y}{x + y}$ - Selling price per kg = 200 - Profit = 25%, so selling price = $1.25 \times C$ - Therefore, $200 = 1.25 \times C \Rightarrow C = \frac{200}{1.25} = 160$ - Set up equation: $\frac{130x + 180y}{x + y} = 160$ - Multiply both sides by $(x + y)$: $130x + 180y = 160x + 160y$ - Rearrange: $180y - 160y = 160x - 130x \Rightarrow 20y = 30x$ - Simplify ratio: $\frac{x}{y} = \frac{20}{30} = \frac{2}{3}$ **Final answers:** - (a)(i) Cost price per kg of mixture = 160 - (a)(ii) Percentage profit = 7.5% - (b) Ratio of mixing type q to type r = 2 : 3