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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 answer is option 'D'. Can you explain this answer?
Verified Answer
P = (40% of A) + (65% of B) and Q = (50% of A) + (50% of B), where A i...
Case I: A = 100, B = 99; A > B
P = (100 × 40%) + (99 × 65%) = 40 + 64.35 = 104.35
Q = (100 × 50%) + (99 × 50%) = 50 + 49.5 = 99.5
⇒ P > Q
Case II: A = 150, B = 100; A > B
P = (150 × 40%) + (100 × 65%) = 60 + 65 = 125
Q = (150 × 50%) + (100 × 50%) = 75 + 50 = 125
⇒ P = Q
Case III: A = 100, B = 50; A > B
P = (100 × 40%) + (50 × 65%) = 40 + 32.5 = 72.5
Q = (100 × 50%) + (50 × 50%) = 50 + 25 = 75
⇒ P = Q
P = (100 × 40%) + (99 × 65%) = 40 + 64.35 = 104.35
Q = (100 × 50%) + (99 × 50%) = 50 + 49.5 = 99.5
⇒ P > Q
Case II: A = 150, B = 100; A > B
P = (150 × 40%) + (100 × 65%) = 60 + 65 = 125
Q = (150 × 50%) + (100 × 50%) = 75 + 50 = 125
⇒ P = Q
Case III: A = 100, B = 50; A > B
P = (100 × 40%) + (50 × 65%) = 40 + 32.5 = 72.5
Q = (100 × 50%) + (50 × 50%) = 50 + 25 = 75
⇒ P = Q
Most Upvoted Answer
P = (40% of A) + (65% of B) and Q = (50% of A) + (50% of B), where A i...
Solution:
Given, P = (40% of A) (65% of B) and Q = (50% of A) (50% of B)
To determine which of the given options is correct, we need to compare P and Q.
Let's simplify both expressions:
P = 0.4A * 0.65B = 0.26AB
Q = 0.5A * 0.5B = 0.25AB
Now, we can see that Q is less than P by only 0.01AB. However, we cannot conclude that P is greater than Q because:
We do not know the actual values of A and B.
Even though A is greater than B, we do not know the magnitude of the difference between them.
Therefore, we cannot say for certain which of the two expressions is greater.
Hence, the correct answer is option 'D': None of the above can be concluded with certainty.
Given, P = (40% of A) (65% of B) and Q = (50% of A) (50% of B)
To determine which of the given options is correct, we need to compare P and Q.
Let's simplify both expressions:
P = 0.4A * 0.65B = 0.26AB
Q = 0.5A * 0.5B = 0.25AB
Now, we can see that Q is less than P by only 0.01AB. However, we cannot conclude that P is greater than Q because:
We do not know the actual values of A and B.
Even though A is greater than B, we do not know the magnitude of the difference between them.
Therefore, we cannot say for certain which of the two expressions is greater.
Hence, the correct answer is option 'D': None of the above can be concluded with certainty.
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P = (40% of A) + (65% of B) and Q = (50% of A) + (50% of B), where A i...
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