There are total 24 hats of blue and red colour. The average cost of blue colour hats is Rs. 65. The average cost of red colour hats is Rs. 35. The average cost of all the hats is Rs. 50. What is the number of red colour hats?

Correct option is A

Given:
Total number of hats = 24
Average cost of blue hats = Rs. 65
Average cost of red hats = Rs. 35
Average cost of all hats = Rs. 50
Solution:
By applying the rule of alligation to the average costs:
Quantity Ratio of Blue hats to Red hats = (50 - 35) : (65 - 50)
Ratio = 15 : 15
Ratio = 1 : 1
This implies that the number of blue hats and red hats are equal.
Total number of hats = 24
Number of red hats = $$\frac{1}{2}$$​ × 24
Number of red hats = 12
Final Answer
So the correct answer is (a)