A shopkeeper mixes two varieties of rice, one costing Tk. 40/kg and other Tk. 60/kg, to create a mixture worth Tk.52/kg. If the total weight of the mixture is 50 kg, determine the quantity of each type of rice used in the mixture.
Let 'x' be the quantity (in kg) of rice costing Tk. 40/kg.
Let 'y' be the quantity (in kg) of rice costing Tk. 60/kg.
Set up Equations:
Equation (i) (Total weight): x + y = 50 (The total weight of the mixture is 50 kg)
Equation (ii) (Total cost): 40x + 60y = 52 × 50 (The total cost of the mixture is the weighted average of the costs of the two types of rice multiplied by the total weight.)
Simplify Equation (ii):
40x + 60y = 2600 [Divide the entire equation by 20 to make it simpler]
⇒ 2x + 3y = 130 ---------(iii)
From Equation (i): x = 50 - y
Substitute this value of x into the simplified Equation (iii):
2(50 - y) + 3y = 130
⇒ 100 - 2y + 3y = 130
∴ y = 30
Substitute the value of y back into the equation x = 50-y:
x = 50 - 30
∴ x = 20
Answer: The shopkeeper used 20 kg of rice costing Tk. 40/kg and 30 kg of rice costing Tk. 60/kg.