P, Q and R can do some work in 11 days, 20 days and 55 days respectively. In how many days can the work be done, if P gets the assistance of Q and R on alternate days?

P fill the tank = 11 days

Q fill the tank = 20 days

R fill the tank = 55 days

Total work done = LCM (11,20,55)= 220

P's efficiency = $$\frac{220}{11}$$ = 20

Q's efficiency = $$\frac{220}{20}$$ = 11

R's efficiency = $$\frac{220}{55}$$ = 4

Tank will be fiiled= $$\frac{220}{35}$$ = 4hours

Tap P is open all the time and taps Q and R are open for one hour each alternately

so

as we know that ,

efficiency multiplied by time = work

here tap P open for T time , meanwhile tap Q And R open alternatively

$$20\times T + 11\times(\frac{T}{2}) + 4\times(\frac{T}{2})$$= 60

27.5T = 220

T = 8 hours