P and O together can make a door in 12 days. They started the work together but after 8 days P left the work. The remaining work is completed by O alone in 7 more days. In how many days can P alone complete the entire work?

Let total work to be done = L.C.M. (12,7) = 84 units

Let efficiency of P and O be $$p$$ and $$o$$ respectively.

=> 1 day work of P and O, $$p+o=\frac{84}{12}=7$$ units/day --------------(i)

According to ques,

=> $$(7\times8)+(o\times7)=84$$

=> $$7o=84-56=28$$

=> $$o=\frac{28}{7}=4$$

Substituting value in equation (i), => $$p=7-4=3$$ units/day

$$\therefore$$ Time taken by P alone = $$\frac{84}{3}=28$$ days

=> Ans - (C)