A can do work alone in 15 days whereas B can destroy entire work in 20 days. They are working on alternate days with a working on the first day, B working on the second day, then how many days will work completed?

To find out how many days it will take for the work to be completed, we need to calculate the combined work done by A and B on each day.

Let's say that the total work to be done is represented as 1 (it can be any unit of measurement).

A can complete the work alone in 15 days, which means A can do 1/15th of the work in a day.

B can destroy the entire work in 20 days, which means B can do -1/20th of the work in a day. Here, the negative sign denotes that B is undoing the work done by A.

Now, let's calculate the combined work done by A and B on each day:

On the first day, A works and completes 1/15th of the work.
On the second day, B works and undoes the work done by A. So, B completes -1/20th of the work.

To find out how many days it will take for them to finish the work, we need to calculate the net work done by A and B on each cycle. The net work done is given by the difference between the work done by A and the work done by B.

Net work done in each cycle = (1/15) - (1/20)

Simplifying, we get:
Net work done in each cycle = (4/60) - (3/60) = 1/60

This means that in each 2-day cycle, 1/60th of the work is completed.

To find out how many cycles it will take to complete the entire work, we need to divide 1 (the total work) by the work done in each cycle:

Number of cycles = 1 / (1/60) = 60

Therefore, it will take 60 cycles (with each cycle taking 2 days) to complete the work.

To find out the total number of days required, we multiply the number of cycles by the number of days in each cycle:

Total number of days = 60 cycles * 2 days/cycle = 120 days

So, it will take 120 days to complete the work.

on any two consecutive days,

1/15 + 1/20 = 7/60 of the job is done
So, after 8 pairs (16) days, 56/60 = 14/15 of the job is done

A finishes the job on day 17.