Difficulty: Medium
Correct Answer: 10%
Explanation:
Introduction / Context:
This question checks the ability to compare two derived quantities that are each a given percentage less than a common base. The important point is to convert each percentage reduction into an explicit expression and then compare the resulting values directly.
Given Data / Assumptions:
Concept / Approach:
First express P and Q in terms of X using percentage reduction. Then compute the difference P minus Q and express this difference as a percentage of P. That gives the percentage by which Q is smaller than P. Choosing a convenient value for X makes the arithmetic more straightforward.
Step-by-Step Solution:
Let X = 100 units for simplicity.P is 20 percent less than X, so P = 100 - 20 = 80 units.Q is 28 percent less than X, so Q = 100 - 28 = 72 units.Difference between P and Q = 80 - 72 = 8 units.Required percentage by which Q is smaller than P = (difference / P) * 100.So percentage = (8 / 80) * 100 = 10 percent.
Verification / Alternative check:
If we take X = 250, then P = 250 * 0.8 = 200 and Q = 250 * 0.72 = 180. Difference is 20. The percentage 20 / 200 * 100 = 10 percent, which again shows that Q is 10 percent smaller than P regardless of the particular value of X.
Why Other Options Are Wrong:
Options 23 percent, 12 percent and 13 percent do not match the exact ratio of the difference to P. They result from dividing by X or by Q instead of P or from misreading the percentage reductions.
Common Pitfalls:
Candidates sometimes subtract the two reduction percentages directly, saying 28 minus 20 equals 8 percent, which is not the answer being asked. The question wants the relative difference between P and Q, not between their reductions from X. Always check which quantities you are comparing.
Final Answer:
Q is 10 percent smaller than P.
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