P alone can do a work in 13 days, Q alone can do the same work in 39 days, R alone can do the same work in 52 days. They start the work together and completed the work such that P and Q was not working on last 1 day. In how many days (total) was the work completed ?

9 days

Let us include their last day work in total work .

P's last day work = + 12

R's last days work = + 3

Total work = 156 + 15 = 171

total work was completed = \(\frac{171}{19}\) = 9 days