A trader mixes two kinds of wheat costing ₹ 40 per kg and ₹ 60 per kg in the ratio of 3:2 and sells half of the mixture at a 25% profit, one-fourth at a 10% loss and the remaining one-fourth at no profit, no loss. The overall profit percentage of the trader is

Correct option is A

Given:
Cost of Wheat A = ₹40/kg
Cost of Wheat B = ₹60/kg
Mixing ratio = 3:2
Half mixture sold at +25%
One-fourth mixture sold at -10%
Remaining one-fourth sold at 0%
Formula Used:
Overall Profit % = Weighted sum of individual profit percentages = $$w_1 P_1 + w_2 P_2 + w_3 P_3$$​​
Solution:
Since the profit percentage does not depend on the absolute cost price per unit, we can find the overall profit directly by taking the weighted average of the profit percentages on the different parts.
Overall Profit % = $$(\frac{1}{2} × 25\%) + (\frac{1}{4} × -10\%) + (\frac{1}{4} × 0\%)$$​​
​$$= 12.5\% - 2.5\% + 0\%$$​​
= 10%
Final Answer
So the correct answer is (a)