Symmetry property in percentages: x% of y is equal to y% of what quantity?
Aptitude
Percentage
Difficulty: Easy
Choose an option
Answer
Correct Answer: x
Explanation
Introduction / Context:This is a well-known symmetry: x% of y equals y% of x. The question asks you to recognize this and state the quantity for which y% produces the same result as x% of y.
Given Data / Assumptions:
- x% of y = (x/100) * y.
- We seek Q such that y% of Q equals the same value.
Concept / Approach:Set (y/100) * Q = (x/100) * y, then solve for Q. Cancellation of y (assuming y ≠ 0) shows the equality directly.
Step-by-Step Solution:
(y/100) * Q = (x/100) * y.Cancel y/100 on both sides ⇒ Q = x.Verification / Alternative check:Numeric example: Let x = 30 and y = 50. Then 30% of 50 = 15. Also, 50% of 30 = 15. Hence, Q must be x.
Why Other Options Are Wrong:
- 100x and x/100 scale the value improperly.
- y/100 and y are unrelated to the required equivalence.
Common Pitfalls:Overcomplicating with extra factors of 100. Keep the percent-as-fraction representation clear.
Final Answer:x