If P and Q together can do a job in 15 days, Q and R together can do it in 12 days and P and R together can do the same in 20 days, then in how many days will the job be completed, if all the three work together?
P+Q = 15 days
Q+R= 12 days
P+R = 20 days
Total work = lcm (15,12,20)= 60 days
(P+Q )'s effiency = $$60\div15$$ =4
(Q+R)'s effiency = $$60\div12$$ =5
(P+R )'s effiency = $$60\div20$$ =3
total efficiency = 2(P+Q+R)= 12
              = (P+Q+R) = 6
time taken = $$work \div efficiency $$
        = $$60 \div 6 = 10 days$$
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