P, Q, R and S can do a piece of work in 20 days. If P and Q together can do it in 50 days, and R alone in 60 days, then in how many days can S alone do it?

P+Q+R+S = 20 days

P+Q = 50 days

R = 60 days

Total work = lcm (20,50,60)= 3000 days

(P+Q +R+S)'s effiency = $$3000\div20$$ =150

(Q+P)'s effiency = $$3000\div50$$ =60

(R)'s efficiency = $$3000\div 60$$ = 50

S efficiency = (P+Q +R+S)'s effiency - (Q+P)'s effiency- (R)'s efficiency

                = 40

S alone do work =  $$\frac{work}{effi}$$

                         $$\frac{3000}{40}$$

                     = 75 days