P can complete five-eighths of a work in 10 days and Q can complete three-fourths of the same work in 9 days. They worked together for 4 days and then P left. How much time will Q working alone, take to complete the remaining work?

5 days

If P completes five - eighths of the work in 10 days, 

Then time taken to complete the total work = 16 days (Apply Unitary Method)

Similarly, 

If Q completes three - fourths of the work in 9 days, 

Then time taken to complete the total work = 12 days

Total work = 48 

Work completed in 4 days = Efficiency x No. Of Days = (3 + 4) x 4 = 7 x 4 = 28

Work left = 48 - 28 = 20

This work will be done by Q alone in = \(\frac{20}{4}\) = 5 days