A and B can do certain work in 18 days and 30 days, respectively. They work together for 5 days. C alone completes the remaining work in 15 days. A and C together can complete $\frac{5}{6}$th part of the same work in:

9 days

A = 18 days,

B = 30 days,

⇒ A + B worked for 5 days = (5 + 3) x 5 = 40 units.  (Efficiency × Days = Total work)

⇒ Remaining work = 90 - 40 = 50 units.

⇒ 50 units was completed by C in 15 days = \(\frac{50}{C}\) = 15 days 

⇒ C = \(\frac{10}{3}\) 

⇒ Time taken by A + C to complete \(\frac{5}{6}\)th work = 90 x \(\frac{5}{6}\) = 75 units,

⇒ \(\frac{75}{5 + 10/3}\) = 9 days.    ..(\(\frac{Work}{Efficiency}\) = Time)