P, Q and R can do a work in 10, 15 and 30 days respectively. P works daily. Q and R together join P on alternate days starting the first day. In how many days will the work be done?

P does 1/10 a day; Q and R together do 1/15 + 1/30 = 1/10. On odd days (all three) 1/5 is done, on even days (P alone) 1/10, so every 2 days 3/10 is done. After 6 days 9/10 is done. On day 7 all three work at 1/5 per day and need 1/10, which takes half a day. Total = 6½ days.