A, B and C can do the same work in 9 days, 12 days and 18 days, respectively. A started the work and worked for 3 days and left. Then, B joined the work and worked for 3 days and left. Then, C joined the work and completed the work. Find the number of days C took to complete the work.

Let the total work be the LCM of 9, 12, and 18, which is 36 units.Efficiency of A = $\frac{36}{9}=4$ units/dayEfficiency of B = $\frac{36}{12}=3$ units/dayEfficiency of C = $\frac{36}{18}=2$ units/dayWork done by A in 3 days = $4\times 3=12$ units.Work done by B in 3 days = $3\times 3=9$ units.Total work completed by A and B = $12+9=21$ units.Remaining work = $36-21=15$ units.Number of days taken by C to complete the remaining work = $\frac{\text{Remaining Work}}{\text{Efficiency of C}}$ $
$\text{Days}=\frac{15}{2}=7\frac{1}{2}\text{ days}$ $