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 $\times$ 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] 

$\Rightarrow$ 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 

$\Rightarrow$ 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.