Rohan and Mohit together can build a wall in 8 days. Mohit and Vikas build the same wall in 10 days and Vikas and Rohan can build the same wall in 12 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.(8,10,12) = 120 units

Let efficiency of Rohan, Mohit and Vikas be $$x,y,z$$ respectively.

Rohan and Mohit together can build the wall in 8 days, => $$x+y=\frac{120}{8}=15$$ units/day ----------(i)

Similarly, $$y+z=\frac{120}{10}=12$$ units/day ----------(ii)

 and $$z+x=\frac{120}{12}=10$$ units/day ----------(iii)

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

=> $$2(x+y+z)=15+12+10=37$$

=> $$x+y+z=\frac{37}{2}$$

$$\therefore$$ Time taken by all of them = $$\frac{120}{\frac{37}{2}}=\frac{240}{37}$$ days

=> Ans - (A)