Mixtures Alligations

To determine the quantity of water to be added to 36 litres of milk so the mixture is worth ₹36 per litre, follow these steps:

1. Identify the initial cost per litre of milk: The total cost for 36 litres is calculated using the given rate (2 ½ litres for ₹120). First, convert 2 ½ litres to a single litre rate:

- Cost for 2.5 litres = ₹120.

- Cost per litre (P) = 120 / 2.5 = ₹48.

2. Set up the equation for the final mixture: Let 'x' be the litres of water added. The total volume of the mixture will be (36 + x) litres with a uniform cost of ₹36 per litre. The total initial cost of milk is 36 * 48 = ₹1728. This cost must equal the final mixture cost:

- Total cost of mixture = (36 + x) * 36.

- Setting the equation: 1728 = (36 + x) * 36.

3. Solve the equation for x:

- 1728 = 1296 + 36x.

- 36x = 432.

- x = 12.

Thus, 12 litres of water must be added.