If 10 litres of oil priced at Rs. 50 per litre are mixed with 5 litres of…

Concept

When two quantities of a substance with different unit prices are mixed, the rate of the resulting mixture is the weighted average of the two prices, weighted by their respective quantities:

Mean Price = (Quantity1 × Price1 + Quantity2 × Price2) ÷ (Quantity1 + Quantity2)

Application

1. Cost of 10 litres of the first oil = 10 × Rs. 50 = Rs. 500.

2. Cost of 5 litres of the second oil = 5 × Rs. 66 = Rs. 330.

3. Total cost of the mixture = Rs. 500 + Rs. 330 = Rs. 830.

4. Total quantity of the mixture = 10 + 5 = 15 litres.

5. Rate of the mixed oil = Total cost ÷ Total quantity = Rs. 830 ÷ 15 = Rs. 55.33 (rounded to two decimals).

Cross-check (alligation rule)

For a mixed rate M, the ratio of the two quantities equals (66 − M) : (M − 50) = 10 : 5 = 2 : 1. So 66 − M = 2(M − 50) → 66 − M = 2M − 100 → 3M = 166 → M = 166 ÷ 3 ≈ Rs. 55.33, confirming the value found above.

Hence, the rate of the mixed oil per litre is Rs. 55.33.