A man wills 25 percent of his wealth to charity and leaves the rest to his family. What percentage of the amount willed to charity does the family receive?

Introduction / Context:
This is a percentage comparison question where we compare one part of a whole with another part, not with the entire amount. The man divides his wealth between charity and family in a simple ratio, and we are asked to express the family share as a percentage of the charity share, not as a percentage of total wealth.

Given Data / Assumptions:
Total wealth = W (some positive amount). Charity receives 25 percent of W. Family receives the remaining 75 percent of W. We need family share expressed as a percentage of the charity share.

Concept / Approach:
When a question asks how much one quantity is as a percentage of another, we use the formula: required percent = (quantity one / quantity two) * 100. Here the quantity one is family wealth and quantity two is charity wealth. Substituting the parts of W gives a simple ratio that we convert into a percentage.

Step-by-Step Solution:
Charity share = 25 percent of W = 25/100 * W = W / 4. Family share = remaining wealth = W - W/4 = 3W/4. We must find family share as a percentage of charity share. So required percent = (family share / charity share) * 100. Substitute: (3W/4) / (W/4) * 100. The W cancels and the 1/4 cancels, giving 3 * 100. Thus required percentage = 300 percent.

Verification / Alternative check:
Take a simple numeric example. Let total wealth W = 100 units. Charity receives 25 units. Family receives 75 units. Now percentage of charity share represented by family share is (75 / 25) * 100 = 3 * 100 = 300 percent. This confirms the result is independent of the actual value of total wealth.

Why Other Options Are Wrong:
Option 200 would correspond to the family getting only double the charity share, which is not correct because 75 is three times 25. Option 33.3 mistakenly interprets charity as a percentage of family share. Option 25 or 75 relate to percentages of total wealth, not to the ratio between family and charity shares. The only correct comparison outcome is 300 percent.

Common Pitfalls:
A typical mistake is to answer 75 or 25 by confusing percentage of total wealth with percentage of the other share. Another pitfall is forgetting which quantity should be the base in the percentage formula. When the question says percentage of the wealth willed to charity, charity must be treated as the base quantity in the denominator of the fraction.

Final Answer:
The family receives an amount equal to 300 percent of the amount willed to charity.