Explanation:

- Start by calculating the work rate:

- 16 boys can complete the work in 28 days.

- Hence, 1 boy can complete the work in \(28 \times 16 = 448\) boy-days.

- Similarly, 12 women can complete the work in 28 days.

- Hence, 1 woman can complete the work in \(28 \times 12 = 336\) woman-days.

- Calculate the combined work rate:

- If 1 boy does \( \frac{1}{448} \) of work per day, then 4 boys do \( \frac{4}{448} = \frac{1}{112} \) of work per day.

- If 1 woman does \( \frac{1}{336} \) of work per day, then 4 women do \( \frac{4}{336} = \frac{1}{84} \) of work per day.

- Work done by 4 boys and 4 women together:

- Combined work rate = \( \frac{1}{112} + \frac{1}{84} = \frac{3}{336} + \frac{4}{336} = \frac{7}{336} = \frac{1}{48} \).

- Time taken for all to complete the work:

- Thus, they will complete the work in 48 days.

- Correct Answer:

- Option 2: 48 days

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