A milkman mixed 10 litres of water (assume the added water was free of cost)…

Concept: When a costlier ingredient is mixed with a cheaper or free one, the cost price of the resulting mixture per unit equals the total cost of all ingredients divided by the total quantity of the mixture: CP(mixture) = Total Cost ÷ Total Quantity. Adding a zero-cost ingredient such as plain water increases the volume without adding any cost, which dilutes the per-unit price below the original rate.

Application:

1. Cost of 50 litres of milk at Rs. 16 per litre = 50 × 16 = Rs. 800.

2. Water is added at zero cost, so the cost of 10 litres of water = Rs. 0; the total cost of the mixture remains Rs. 800.

3. Total volume of the mixture = 50 + 10 = 60 litres.

4. Cost price of the mixture per litre = Total cost ÷ Total volume = 800 ÷ 60 = Rs. 13.33 (rounded to two decimal places).

Cross-check: By alligation, since water is free (cost = 0) and milk costs Rs. 16 per litre, the mean price of the mixture = 16 × (milk's share of total volume) = 16 × (50/60) = Rs. 13.33, confirming the direct calculation.