X and Y can do a piece of work in 72 days. Y and Z can do it in 120 days. X and Z can do it in 90 days. How many days does it take if all the three can work together?
Work done by X and Y in one day = 172…(1)
Work done by Y and Z in one day = 1120…(2)
Work done by Z and X in one day = 190…(3)
(1) + (2) + (3) gives,
2(X+Y+Z)=172+1120+190⟹2(X+Y+Z)=5+3+4360=12360=130
∴ Work done by A, B and C together in one day work =12×130=160
∴ A, B and C will together complete the work in 60 days.