P, Q and R can complete a work in 12, 9 and 15 days respectively. Working together, they will complete the same work in:

$3\frac{39}{47}$days

Let us assume the total work as LCM of 12, 9 and 15 i.e 180 units.

Hence P will do \(\frac{180}{12}\) = 15 units/day

Q will do \(\frac{180}{9}\) = 20 units/day

R will do \(\frac{180}{15}\) = 12 units/day.

Working together, they will do 15 + 20 + 12 = 47 units in a single day.

Hence total time taken to complete the work = \(\frac{180}{47}\) =$3\frac{39}{47}$days.