Explanation:

- Let's define the work rates:

- Let \( B \) be the work rate of one boy.

- Let \( G \) be the work rate of one girl.

- From the problem:

- \( 4B + 6G \) (work for 10 days) = 1 complete work.

- \( 12B + 8G \) (work for 4 days) = 1 complete work.

- Set up equations based on above:

- \( 10(4B + 6G) = 1 \)

- \( 4(12B + 8G) = 1 \)

- Solve the system of equations to find \( B \) and \( G \).

- Calculate combined work rate for 20 boys and 30 girls:

- Work rate = \( 20B + 30G \)

- Compute time for full work:

- Total work / Total work rate = Time taken

- After calculations, you'll find it takes 2 days for 20 boys and 30 girls.

So, the correct answer is:

- Option 1: 2 days