720 sweets are shared equally among children such that each child receives a number of sweets equal to 20% of the total number of children. How many sweets does each child get?

Introduction / Context:
The number of sweets per child depends on the number of children, and the problem links them: each child’s share is 20% of the headcount. This yields a quadratic relation in the number of children.

Given Data / Assumptions:

• Total sweets = 720.
• If number of children = n, then sweets per child = 0.20 * n.
• All sweets are distributed exactly.

Concept / Approach:
Total sweets = (children) * (sweets per child) = n * (0.20n) = 0.20n^2. Set that equal to 720 and solve for n. Then compute each child’s share using 0.20n.

Step-by-Step Solution:

Verification / Alternative check:
Total sweets check: 60 children * 12 sweets = 720, consistent.

Why Other Options Are Wrong:
14, 11, 15, 10 do not satisfy the quadratic relationship when multiplied by the corresponding child count.

Common Pitfalls:
Treating 20% of children as 20% of sweets, or assuming a linear relation. The share per child depends on n, producing n^2.

Final Answer:
12