A Can Do a Piece of Work in 12 Days. When He Had Worked for 2 Days B Joins Him. If the Complete Work was Finished in 8 Days, in How Many Days B Alone Can Finish the Work?

A can do a piece of work in 12 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days, in how many days B alone can finish the work?

Total number of days A will take to complete the work = 12

The work was completed in 8 days.

So, the work done by A in 8 days = 8 / 12 = 2 / 3

Let’s take the total work as 1.

The remaining work which was done by B = 1 - (2 / 3)

==> (3 - 2) / 3

==> 1 / 3

Here B is joining the work 2 days after A started the work.

So, the number of days B worked = 8 - 2 = 6

To find the number of days B would take to complete the work alone, you need to divide the work done by B from the number of working days.

==> 6 / (1 / 3)

==> 6 (3) = 18

The number of days B needs to finish the work is 18 days.

Explanation of the Method

In this problem, we need to calculate the number of days that person B takes to complete a work alone. We have used the concepts of work done and time to solve the problem.

We had to determine the work done by A and B separately. By breaking down the whole work done by the two people as fractions, we can find the solution to this problem.