If P=(40% of A)+(65% of B) and Q=(50% of A)+(50% of B), where A is greater than B. In this context which of the following statements is correct?

Correct option is D

Given:
P = 0.40A + 0.65B
Q = 0.50A + 0.50B
A > B
Formula Used:
Compare the values by finding the difference Q - P or P - Q.
Solution:
Calculate the difference Q - P:
Q - P = (0.50A + 0.50B) - (0.40A + 0.65B)
Q - P = 0.10A - 0.15B
Since A > B, the result of 0.10A - 0.15B depends on how much larger A is compared to B.
Case 1: Let A = 2B. Then Q - P = 0.10(2B) - 0.15B = 0.20B - 0.15B = 0.05B (Q > P).
Case 2: Let A = 1.1B. Then Q - P = 0.10(1.1B) - 0.15B = 0.11B - 0.15B = -0.04B (P > Q).
Since both cases are possible, no certain conclusion can be drawn.
Final Answer
So the correct answer is (d)