P and Q can do a work in 10 days. Q and R can do it in 12 days. All three together can finish in 8 days. In how many days can P and R can complete the work?
P+Q = 10 days
Q+R= 12 days
P+Q+R = 8 days
Total work = lcm (10,12,8)= 240 days
(P+Q )'s effiency = $$240\div10$$ =24
(Q+R)'s effiency = $$240\div12$$ =20
(P+Q+R)'s efficiency = $$240\div 8$$Â = 30
total efficiency = 2(Q+P+R)+Q = 74
            = 2(30) + Q = 74
            = Q = 14
P+Q = 24
P + 14 = 24
P = 10
P+Q+R = 30
10+ 14+ R = 30
R = 6
(P+R) time taken = $$work\div effi $$Â
             = $$240\div 16 $$Â
(P+R) time taken = 15 days
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