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 = $$240\div 8$$  = 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 = $$work\div effi $$ 

                          = $$240\div 16 $$ 

(P+R) time taken = 15 days