P and Q together complete a work in 8 days. Q and R together complete a work in 16 days and R and P together complete the same work in 8 days. In how many days P, Q and R together can complete the wok?

Let total work is L.C.M. (8,16,8) = 16 units

Let efficiency of P, Q and R respectively be $$p,q,r$$ units/day

P and Q together can complete the work in 8 days, => (P+Q)'s efficiency = $$p+q=\frac{16}{8}=2$$ units/day -------------(i)

Similarly (Q+R)'s efficiency = $$q+r=\frac{16}{16}=1$$ unit/day ------------(ii)

and  (R+P)'s efficiency = $$r+p=\frac{16}{8}=2$$ units/day ----------------(iii)

Adding equations (i), (ii) and (iii), we get : $$2(p+q+r)=2+1+2$$

=> $$(p+q+r)=\frac{5}{2}=2.5$$ -----------(iv)

$$\therefore$$ Days required by P, Q and R together to complete the work = $$\frac{16}{2.5}=6.4$$ days

=> Ans - (A)