In what ratio must water be mixed with milk costing Rs. 12 per liter to obtain a mixture worth Rs. 8 per liter?

Let the quantity of water be x liters and the quantity of milk be y liters.

Given:
1. Cost of milk = Rs. 12 per liter
2. Cost of mixture = Rs. 8 per liter

For the mixture to be worth Rs. 8 per liter, the weighted average of the costs of water and milk should be Rs. 8.

The cost of water is Rs. 0 (since it's not charged), and the cost of milk is Rs. 12 per liter.

Now, the equation for the weighted average is:

$\mathrm{Cost} \mathrm{of} \mathrm{mixture} = \frac{\mathrm{Total} \mathrm{cost} \mathrm{of} \mathrm{water} + \mathrm{total} \mathrm{cost} \mathrm{of} \mathrm{milk}}{\mathrm{Total} \mathrm{water} \mathrm{quantity} + \mathrm{total} \mathrm{milk} \mathrm{quantity}}$

Given the cost of the mixture is Rs. 8 and the cost of milk is Rs. 12, we can set up the equation:

$8=\frac{0\times \mathrm{x}+12\times \mathrm{y}}{\mathrm{x}+\mathrm{y}}$

Simplify the equation:

$\Rightarrow 8(\mathrm{x}+\mathrm{y})=12\mathrm{y}$

$\Rightarrow 8\mathrm{x}+8\mathrm{y}=12\mathrm{y}$

$\Rightarrow 8\mathrm{x}=4\mathrm{y}$

$\Rightarrow 2\mathrm{x}=\mathrm{y}$

$\Rightarrow \frac{\mathrm{x}}{\mathrm{y}}=\frac{1}{2}$

This gives us the ratio of water to milk x : y = 1 : 2

Therefore, the water should be mixed with milk in the ratio 1 : 2 to obtain a mixture worth Rs. 8 per liter.