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:

Let the total work = 360 units

Efficiency of A = $$\frac{360}{18}$$ = 20 units/day

Efficiency of B = $$\frac{360}{30}$$ = 12 units/day

A and B worked together for 5 days.

Work done by A and B together in 5 days = 5 x (20 + 12) = 160 units

Remaining work = 360 - 160 = 200 units

C alone completes the remaining work in 15 days.

Efficiency of C = $$\frac{200}{15}$$ = $$\frac{40}{3}$$ units/day

Efficiency of A and C together = 20 + $$\frac{40}{3}$$ = $$\frac{100}{3}$$ units/day

$$\frac{5}{6}$$th of the total work = $$\frac{5}{6}\times$$360 = 300 units

Number of days required for A and C together to complete $$\frac{5}{6}$$th of work = $$\frac{300}{\frac{100}{3}}$$

= $$\frac{300\times3}{100}$$

= 9 days

Hence, the correct answer is Option C