18 workers can complete a piece of work in 96 days. They start working together and after 26 days 10 more workers join them. In how many days in all will the work be completed?

To find the total number of days required to complete the work, we can analyze the total work in terms of "worker-days".

Step 1: Calculate the total work.
It is given that 18 workers can complete the work in 96 days.
Total Work = Number of workers × Number of days
Total Work = $18\times 96$ = 1728 worker-days.

Step 2: Calculate the work completed in the first 26 days.
The initial 18 workers work together for 26 days before any changes occur.
Work done in 26 days = $18\times 26$ = 468 worker-days.

Step 3: Find the remaining work.
Remaining Work = Total Work - Work Completed
Remaining Work = 1728 - 468 = 1260 worker-days.

Step 4: Calculate the new number of workers.
After 26 days, 10 more workers join the existing 18 workers.
New number of workers = 18 + 10 = 28 workers.

Step 5: Calculate the remaining days needed to finish the work.
Let the remaining work be completed by the 28 workers in $d$ days.
Remaining Work = New number of workers × $d$
$1260=28\times d$
$d=\frac{1260}{28}$
$d=45$ days.

Step 6: Calculate the total days in all to complete the work.
Total days = Days worked initially + Remaining days
Total days = 26 + 45 = 71 days.

Thus, the work will be completed in 71 days in all.