A, B and C can complete a certain work in $12$, $15$ and $20$ days, respectively. A and B together start the work and B leaves after working for $4$ days. A and C together will complete the remaining work in ______ days.

Let's find the total work by taking the Least Common Multiple (LCM) of the days taken by A, B, and C.
$$\text{Total Work}=\text{LCM}(12,15,20)=60\text{ units}$$
Now, let's find the daily efficiency of each individual:Efficiency of A = $\frac{60}{12}=5\text{ units/day}$ Efficiency of B = $\frac{60}{15}=4\text{ units/day}$ Efficiency of C = $\frac{60}{20}=3\text{ units/day}$ Step 1: Work done by A and B together for 4 daysCombined efficiency of A and B = $5+4=9\text{ units/day}$ Work done in 4 days = $9\times 4=36\text{ units}$ Step 2: Calculate remaining workRemaining work = $60-36=24\text{ units}$ Step 3: Time taken by A and C to finish remaining workCombined efficiency of A and C = $5+3=8\text{ units/day}$ Time taken by A and C = $\frac{\text{Remaining work}}{\text{Efficiency of A+C}}=\frac{24}{8}=3\text{ days}$