405 sweets were distributed equally among children in such a way that each child gets `20%` of the total number of children. How many sweets did each child get?

Options

A. 15
B. 45
C. 9
D. 18

Answer

To solve the problem, we need to determine how many sweets each child receives when 405 sweets are distributed equally among children, with each child receiving 20% of the total number of children.

### Step-by-Step Solution:

1. **Let the number of children be represented as \( x \)**.
- We know that each child receives 20% of the total number of children. Therefore, the amount each child receives can be expressed as \( 0.2x \).

2. **Set up the equation based on the total number of sweets**:
- Since the total number of sweets distributed is 405, we can write the equation:
\[ x \cdot (0.2x) = 405 \]

3. **Simplify the equation**:
- This simplifies to:
\[ 0.2x^2 = 405 \]

4. **Multiply both sides by 5 to eliminate the decimal**:
\[ x^2 = 405 \cdot 5 \]
\[ x^2 = 2025 \]

5. **Take the square root of both sides to find \( x \)**:
\[ x = \sqrt{2025} \]
\[ x = 45 \]

6. **Now, calculate how many sweets each child gets**:
- Each child receives \( 0.2x \):
\[ \text{Sweets per child} = 0.2 \cdot 45 = 9 \]

### Final Answer:
Each child gets **9 sweets**.