Symmetry property in percentages: x% of y is equal to y% of what quantity?

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:

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