2 printing machine of a printing house can complete in 20 days. After printing the book for 8 days, If 1 machine was added the remaining work can be complete?

If two printing machines can complete the work in 20 days, we can assume that each machine contributes equally to the printing process. Therefore, we can say that the work done by two machines in a single day is equal to 1/20th of the total work.

Let's denote the total work as W. In 20 days, two machines complete the entire work, so the work done by two machines in a single day is W/20.

If the machines worked for 8 days, the work completed by two machines in that time would be 8 * (W/20) = 8W/20 = 2W/5.

Now, we need to determine if adding one machine will be sufficient to complete the remaining work. Let's assume that the remaining work to be completed is R.

With the addition of the third machine, the work done by three machines in a single day will be 3/20th of the total work. Therefore, in 1 day, the work completed by three machines would be 3W/20.

If the machines worked for x days after the addition of the third machine, the work completed by three machines in that time would be x * (3W/20) = 3xW/20.

We know that after 8 days, the work completed is 2W/5. Therefore, the remaining work is R = W - 2W/5 = 3W/5.

To find the number of days required to complete the remaining work with three machines, we equate the work completed with the remaining work:

3xW/20 = 3W/5.

Canceling out the common terms, we get:

x/20 = 1/5.

Cross-multiplying, we find:

5x = 20.

Dividing both sides by 5:

x = 4.

Therefore, it would take an additional 4 days for the three machines to complete the remaining work.