Raja and Kundan together can build a wall in 20 days, Kundan and Mahesh build the same wall in 30 days and Mahesh and Raja can build the same wall in 24 days. In how many days can all the three complete the same wall while working together?

Let total work to be done = L.C.M.(20,30,24) = 120 units

Let efficiency of Raja, Kundan and Mahesh be $$x,y,z$$ respectively.

Raja and Kundan together can build the wall in 20 days, => $$x+y=\frac{120}{20}=6$$ units/day ----------(i)

Similarly, $$y+z=\frac{120}{30}=4$$ units/day ----------(ii)

 and $$z+x=\frac{120}{24}=5$$ units/day ----------(iii)

Adding equations (i), (ii) and (ii), we get :

=> $$2(x+y+z)=6+4+5=15$$

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

$$\therefore$$ Time taken by all of them = $$\frac{120}{7.5}=16$$ days

=> Ans - (B)