X and Y, working together, can complete a work in 30 days, Y and Z, working together, can complete the same work in 40 days. and Z and X, working together, can complete the same work in 24 days. In how many days can X, Y and Z, working together, complete the work?

20 days

X + Y = 30 days,

Y + Z = 40 days,

Z + X = 24 days,

⇒ Adding all the efficiencies,

⇒ 2(X + Y + Z) = 12,

⇒ X + Y + Z = 6,

⇒ Time required by X + Y + Z to complete the work = \(\frac{120}{6}\) = 20 days,   ..(\(\frac{Work}{Efficiency}\) = Time)