If x is 80% of y, then y is what percent of 2x?

Introduction:
This algebraic percentage question examines how well you manipulate relationships between two variables expressed in percentage form. It is common in aptitude tests to relate variables using percentages and then ask for one variable as a percentage of some linear combination of the other.

Given Data / Assumptions:
x is 80% of y.
We need to find y as a percentage of 2x.
The variables x and y are positive real numbers.

Concept / Approach:
The statement x is 80% of y means x = 0.80 * y. Once we have this relationship, we can express 2x in terms of y, and then find the fraction y / (2x). Converting this fraction into a percentage gives the required answer. The key tools are substitution and basic fraction handling.

Step-by-Step Solution:
Given that x is 80% of y. Write this as an equation: x = 80% of y = 0.80 * y. We are asked for y as a percentage of 2x. First express 2x in terms of y: 2x = 2 * (0.80 * y). So 2x = 1.60 * y. We now want to find y / (2x) expressed as a percentage. Compute y / (2x) = y / (1.60 * y). Cancel y from numerator and denominator (since y is not zero): y / (1.60 * y) = 1 / 1.60. 1 / 1.60 = 0.625. Convert 0.625 to a percentage by multiplying by 100. 0.625 * 100 = 62.5%.
Verification / Alternative check:
Use assumed values to confirm. Let y = 100. Then x is 80% of 100, so x = 80. Then 2x = 160. Now y as a percentage of 2x is (100 / 160) * 100 = 62.5%, which matches the algebraic answer. Using concrete numbers helps confirm that no algebraic mistake has been made.

Why Other Options Are Wrong:
Values like 56.5%, 60%, 64.5%, and 66.5% arise from incorrect arithmetic or errors in setting up the fraction. For example, some might compute x / (2y) or treat 80% as 0.8 in an incorrect place. Only 62.5% corresponds correctly to the relationship x = 0.80 * y and the requirement to express y as a percentage of 2x.

Common Pitfalls:
A common error is to assume that if x is 80% of y, then y is automatically 80% of 2x, which is not true. Percentages always depend on which quantity is taken as the base. Another mistake is mixing up which variable should be in the numerator or denominator when forming the fraction that is to be converted to a percentage.

Final Answer:
y is 62.5% of 2x.