If X = 600 and Y = 800, then X is how many percent less than Y?

Introduction / Context:
This is a direct percentage comparison problem. The task is to find by what percentage one number is less than another given number. Such questions frequently appear as warm up questions in percentage sections.

Given Data / Assumptions:

• X = 600.
• Y = 800.
• We need to find the percentage by which X is less than Y.

Concept / Approach:
To find how much X is less than Y in percentage terms, we compute the difference Y minus X and then divide that difference by Y, because Y is the reference quantity. Finally, we multiply by 100 to convert the fraction into a percentage.

Step-by-Step Solution:
Y = 800 and X = 600.Difference between Y and X = 800 - 600 = 200.Required percentage less = (difference / Y) * 100.So percentage = (200 / 800) * 100.Compute 200 / 800 = 0.25.Therefore, percentage less = 0.25 * 100 = 25 percent.

Verification / Alternative check:
We can think in terms of fractions. X / Y = 600 / 800 = 3/4. This means X is 75 percent of Y, so it is lacking 25 percent to reach Y. Thus X is 25 percent less than Y, confirming the computed result.

Why Other Options Are Wrong:
33.33 would correspond to a one third reduction, which does not match the actual ratio. The value 75 is the fraction of Y that X represents, not how much it is less by. The value 35 is simply an arbitrary incorrect choice.

Common Pitfalls:
A typical mistake is to divide the difference by X instead of Y, which would answer a different question, namely how much Y is greater than X. Always pay attention to which number your percentage comparison is based on.

Final Answer:
X is 25 percent less than Y.