A seller mixed 4 dozen bananas costing Rs.12 per dozen with 6 dozen bananas at…

Concept

The mean (average) price of a mixture made by combining two quantities at two different prices is found by the alligation/weighted-average rule: Mean Price = (Total Cost of All Parts) / (Total Quantity) = (q1*p1 + q2*p2) / (q1 + q2).

Application

1. Cost of the first part: 4 dozen bananas at Rs. 12 per dozen = 4 x 12 = Rs. 48.

2. Cost of the second part: 6 dozen bananas at Rs. 8 per dozen = 6 x 8 = Rs. 48.

3. Total cost of the mixture = Rs. 48 + Rs. 48 = Rs. 96.

4. Total quantity of the mixture = 4 dozen + 6 dozen = 10 dozen.

5. Mean price per dozen = Total cost / Total quantity = 96 / 10 = Rs. 9.6 per dozen.

Cross-check (alligation ratio form)

1. The ratio (quantity at Rs. 8) : (quantity at Rs. 12) = 6 : 4 = 3 : 2.

2. By the alligation rule this ratio equals (Rs. 12 - mean) : (mean - Rs. 8), so 3(mean - 8) = 2(12 - mean).

3. Expanding: 3*mean - 24 = 24 - 2*mean.

4. So 5*mean = 48, giving mean = Rs. 9.6 - the same value, confirming the answer independently.

Result

The cost price of the mixed bananas is Rs. 9.6 per dozen.