P and Q together can complete a work in 105 days. Q and R together can complete the same work in 90 days, P and R together can complete the same work in 126 days. In how many days P, Q and R together can complete the same work?
Let the total work be 1890 units (LCM of 105, 90 and 126)
Efficiency of P+Q = 1890/105 = 18 units per day
Efficiency of Q+R = 1890/90 = 21 units per day
Efficiency of P+R = 1890/126 = 15 units per day
Total efficiency of 2(P+Q+R) = 54 units per day
Efficiency of (P+Q+R) = 27 units per day
Therefore, P, Q and R can do the work together in $$\dfrac{1890}{27} = 70$$ days.
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