A man wills 40 percent of his wealth to his wife and the remaining 60 percent to his children. The wealth received by the children is what percentage of the wealth willed to the wife?

Introduction / Context:
This is a ratio and percentage comparison question. It asks you to compare the share of one group (children) to the share of another group (wife) in terms of percentage. Problems like this are common in profit sharing, inheritance, and partnership distributions.

Given Data / Assumptions:
- Total wealth is assumed to be 100 units for simplicity.
- Wife receives 40 percent of the wealth, so her share = 40 units.
- Children together receive the remaining 60 percent, so their share = 60 units.
- We must express the children's share as a percentage of the wife's share.

Concept / Approach:
To express one quantity as a percentage of another, divide the first quantity by the second and multiply by 100. Here, the children's share must be divided by the wife's share and then expressed as a percentage. Using a base total of 100 makes the arithmetic very straightforward and preserves all ratios.

Step-by-Step Solution:
Step 1: Assume total wealth = 100 units.Step 2: Wife's share = 40 percent of 100 = 40 units.Step 3: Children's combined share = 100 - 40 = 60 units.Step 4: To find percentage of wife's share represented by children's share, compute (Children's share / Wife's share) * 100.Step 5: Substitute values: (60 / 40) * 100.Step 6: Simplify 60 / 40 = 3 / 2 = 1.5.Step 7: Therefore, percentage = 1.5 * 100 = 150 percent.

Verification / Alternative check:
You can also think of it as a ratio. The wife:children ratio is 40:60, which simplifies to 2:3. This means children's share is 1.5 times the wife's share. A quantity that is 1.5 times another is 150 percent of it, because 1.5 equals 150 percent when written as a percentage. This matches the algebraic method.

Why Other Options Are Wrong:
- 66.6 percent and 50 percent correspond to reverse or incorrect comparisons; they do not represent how much greater 60 is relative to 40.
- 20 percent is far too small and would mean the children receive much less than the wife, which contradicts the given division of 40 percent and 60 percent.

Common Pitfalls:
A typical confusion is mixing up "percentage of total wealth" with "percentage of another person's share." The children receive 60 percent of total wealth, not 60 percent more than the wife. Another error is comparing the wife's share to the children's share instead of the other way around, which would lead to 66.6 percent. Always check which quantity needs to be expressed as a percentage of which base.

Final Answer:
The children receive 150 percent of the wealth willed to the wife.