I can think about two approach below.

Please check it out. It may be helpful.

A can build a house in 20 days. And B can break it in 30 days.

METHOD -1Lets take LCM of (20,30) = 60 . 60 be the unit of work to do.

A works on 1st day and B on 2nd day and so on.

Day 1 -In 1 day A can finish - 60/20 = 3 unit of work.

Day 2 -In 1 day B can break- 60/30 = 2 unit of work.

So after day 2. Total work that was done - 1 unit of work.

Implies, it will take 120 days to complete - 60 unit of work.

=> Here is the most important part of the question. => (Assume once the house gets build, they will stop working)Lets think about it. Try to go in reverse gear.

B completed - 120 days -> 60 unit of work.

A completed - 119 days -> 62 unit of work = 60+2 (work done by B on 120th day).

B completed - 118 days -> 59 unit of work = 62 -3 (work done by B on 119th day).

A completed - 117 days -> 61 unit of work = 59 + 2 (work done by B on 118th day).

B completed - 116 days -> 58 unit of work. = 61 - 3 (work done by A on 117th day).

A completed - 115 days -> 60 unit of work. = 58 + 2 (work done by B on 116th day).

Answer - B => 115 days.METHOD -2We can do it directly in a go if we use our visualization skill.

Lets take LCM of (20,30) = 60 . 60 be the unit of work to do.

A works on 1st day and B on 2nd day and so on.

Day 1 -In 1 day A can finish - 60/20 = 3 unit of work.

Day 2 -In 1 day B can break- 60/30 = 2 unit of work.

So after day 2. Total work that was done - 1 unit of work.

Implies, it will take 120 days to complete - 60 unit of work.

But we need to realize that there is possibility of A completing the work before 120 DAYS as A is doing positive work.

Lets consider after 110 days.

After 110 days. Total work done is - 55.

After 112 days. Total work done is - 56.

After 114 days. Total work done is - 57.

Now hold on.

A can finish 3 unit of work in a day.

=> After 115 days. Total work done is - 60.

Answer B => 115.
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Thank You

Sudhanshu