X alone can do a piece of work in 15 days. Y alone can do the same work in 30 days. X, Y and Z, working together, can complete the work in nine days. In how many days Z alone can complete the same work?

90

X = 15 days, Y = 30 days, X + Y + Z = 9 days,

⇒ X + Y + Z = 10  (Efficiency)

⇒ 6 + 3 + Z = 10

⇒ Z = 10 - 9 

⇒ Z = 1,

Therefore, time required for Z alone to complete the work = \(\frac{90}{1}\) = 90 days,     ..(\(\frac{Work}{Efficiency}\) = Time)