Step-by-step Solution:

Quick Solution

This problem can be solved by translating the given information into a simple algebraic equation.

1. Set Up the Equation

• Let the number of children in the group be C.
• The problem states that "the number of sweets received by each child is one-fifth of the number of children". So, the number of sweets per child can be written as C / 5.

The total number of sweets distributed is found by multiplying the number of children by the number of sweets each one receives. We are told this total is 405.

(Number of Children) × (Sweets per Child) = Total Sweets
C × (C / 5) = 405

2. Solve for the Number of Children (C)

Now, we can solve this equation for C:

C² / 5 = 405
C² = 405 × 5
C² = 2025
C = √2025
C = 45

3. Verification (Optional)

- If there are 45 children...
- ...then each child receives 45 / 5 = 9 sweets.
- The total sweets distributed would be 45 children × 9 sweets/child = 405. This matches the information given in the problem.

Final Answer: The number of children in the group is 45.