Explanation:

To determine how many days 14 persons working 8 hours a day would take to complete the work, we first calculate the total work done in person-hours using the initial setup:

- Initial Setup:

- 18 persons work for 7 hours a day.

- They complete the work in 32 days.

- Total work = 18 persons × 7 hours/day × 32 days = 4032 person-hours.

- New Scenario:

- 14 persons work for 8 hours a day.

- Let's calculate how many days (denoted as 'D') it would take.

- Total work = 14 persons × 8 hours/day × D days = 4032 person-hours.

- Solving for D:

- $14\times 8\times D=4032$

- $112\times D=4032$

- $D=\frac{4032}{112}$

- $D=36$

- Correct Answer: Option 4 - 36 days

Option 4: 36 days is the correct choice.

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