Two numbers X and Y are respectively 20% and 28% less than a third number Z. By what percentage is Y less than X?

Introduction / Context:
This is a comparative percentage question with a common reference. Converting all numbers to the same base (Z) allows a direct comparison between X and Y, and then we compute the relative percentage difference with X as the base since we are asked “Y less than X.”

Given Data / Assumptions:
Let Z = 100 units for convenience. Then X = 80 (20% less), Y = 72 (28% less).

Concept / Approach:
Required percent = (X − Y) / X * 100. Using the normalized values avoids carrying Z through algebra and leads to quick computation.

Step-by-Step Solution:

Verification / Alternative check:
Proportional reasoning: Y/X = 72/80 = 0.9, so Y is 90% of X, meaning it is 10% less.

Why Other Options Are Wrong:
8% and 9% are near but not exact; 12% overshoots; 7.5% has no basis in the given reductions.

Common Pitfalls:
Comparing both directly to Z and then subtracting the percentages (28% − 20% = 8%) without converting to the same base for the final comparison. The reference for “less than X” must be X.

Final Answer:
10%