### Solution:

Concept: A and B can finish a task in 12 days when working together. Determine how much work A and B accomplished in one day, X. The task can be finished by A alone in 20 days. Only use A say Y to calculate the amount of work completed in a day.To find the quantity of work that B can complete in a single day, subtract y from x. Exchange z to learn how many days B alone will need to complete the task, let's say a. If he works half a day, then B will have twice as many days, let's say two. Add and a to get the required value.

We are given and together we can complete a work in 12 days.

The work done by and together in a day will be We are also given A alone to finish the work in 20 days.

The work done by only in a day will be Subtract from to get the work done by only B in a day.

B B B Therefore, B alone can finish of the work in one day.

This means B alone takes 30 days to finish the total work.

When B works half a day then he will take days to finish the total work.

When A works full day and B works half day then the work which will be finished in one day will be

A and B can together finish th of the work in one day, this means when A works full day and B works half day then it takes 15 days to finish the total work.

Hence, the correct answer is Option (1).