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?
(a) P is greater than Q.
(b) Q is greater than P.
(c) P is equal to Q.
(d) None of the above can be concluded with certainty.
Correct option (d) None of the above can be concluded with certainty.
Explanation:
According to the question, P = (40% of A) + (65% of B) and
Q = (50% of A) + (50% of B), where A > B
Now, P – Q = (40% of A) + (65% of B) – (50% of A) – (50% of B) = (15% of B) – (10% of A)
We know that A > B, but not by how much.
Hence, all three cases are possible, as illustrated below:
1. If B = 100 and A = 110, then P – Q = (15% of B) – (10% of A) = 15 – 11 = 4. So, P > Q
2. If B = 100 and A = 150, then P – Q = (15% of B) – (10% of A) = 15 – 15 = 0. So, P = Q
3. If B = 100 and A = 200, then P – Q = (15% of B) – (10% of A) = 15 – 20 = -5. So, P < Q Hence, nothing can be said about the relation between P and Q.