Amit and Sunil together can complete a work in 9 days, Sunil and Dinesh together can complete the same work in 12 days, and Amit and Dinesh together can complete the same work in 18 days. In how many days will they complete the work if Amit, Sunil and Dinesh work together?

8 days

Amit (A) + Sunil (S) = 9 days,

Sunil (S) + Dinesh (D) = 12 days,

Amit (A) + Dinesh (D) = 18 days,

⇒ Adding all three efficiencies, 

⇒ 2 (A + S + D) = 9

⇒  (A + S + D) = 4.5

⇒ Time taken by (A + S + D) to complete total work = \(\frac{36}{4.5}\) = 8 days.      ..(\(\frac{Work}{Efficiency}\) = Time)