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?
Answer & explanation
Correct answer: option 4
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)