Aman and Raman together complete a piece of work in 30 days, Raman and Manan can complete the same work in 36 days and Manan and Aman can complete the same work in 45 days. All of the three working together can complete the work in how many days?

Let total work to be done = L.C.M. (30,36,45) = 180 units

Let efficiency of Aman, Raman and Manan be $$x,y$$ and $$z$$ units/day respectively.

Aman and Raman together complete a piece of work in 30 days, => $$(x+y)=\frac{180}{30}=6$$ units/day

Similarly, $$(y+z)=5$$ and $$(z+x)=4$$

Adding all the equations, we get : $$2(x+y+z)=6+5+4=15$$

=> $$(x+y+z)=\frac{15}{2}=7.5$$

$$\therefore$$ Time taken by all of them working together = $$\frac{180}{7.5}=24$$ days

=> Ans - (C)