P, Q and R can do a piece of work in 45, 30 and 22.5 days respectively. P is assisted by Q on one day and R on the next day alternatively. How long would the work take to finish?

16\(\frac{2}{5}\) days

1st day work by (P + Q) = 2 + 3 = 5

2nd day work by (P + R) = 2 + 4 = 6

2 days work = 11

16 days work = 88

Remaining work = 90 - 88 = 2

So, remaining work will be done by (P + Q) in = \(\frac{2}{5}\) days.

Therefore, the work will be finished in = 16\(\frac{2}{5}\) days