Explanation:

- Given Information:

- 4 boys or 7 girls complete the work in 18 days.

- Need to find out how long 12 boys and 21 girls will take.

- Calculating Total Work:

- Let 1 boy's 1-day work = \(b\), and 1 girl's 1-day work = \(g\).

- \(4b = 7g\).

- Total work = \(4b \times 18 = 72b\) or \(7g \times 18 = 126g\).

- Calculating Combined Rate of Work:

- The combined 1-day work of the group is \(12b + 21g\).

- Substitute \(g = \frac{4}{7}b\) using \(4b = 7g\).

- \(12b + 21g = 12b + 21 \times \frac{4}{7}b = 12b + 12b = 24b\).

- Calculating Days Required:

- Total days = \(\frac{Total Work}{Combined Rate of Work}\).

- \(\frac{72b}{24b} = 3\) days.

- Correct Answer:

- Option 1: 3 days