Three decorators, A, B, and C, can complete a mural individually in 5 days, 16 days, and 20 days, respectively. They work together for 2 days. After that, A leaves, while B and C continue for only $\frac{1}{2}$ of their usual daily working time. How many additional days will they need to complete the mural?

The correct option is $6\frac{2}{3}$ days.

Step 1: Determine the individual daily work rates of each decorator.
Let the total work required to complete the mural be equal to 1 unit.
Decorator A can complete the mural in 5 days, so A's work done per day is:
$\frac{1}{5}$
Decorator B can complete the mural in 16 days, so B's work done per day is:
$\frac{1}{16}$
Decorator C can complete the mural in 20 days, so C's work done per day is:
$\frac{1}{20}$

Step 2: Calculate the work completed when all three work together for 2 days.
The combined daily work rate of A, B, and C working together is:
$\frac{1}{5}+\frac{1}{16}+\frac{1}{20}$
To add these fractions, we find the Least Common Multiple (LCM) of the denominators (5, 16, and 20), which is 80:
$\frac{16+5+4}{80}=\frac{25}{80}=\frac{5}{16}$
So, working together, they complete $\frac{5}{16}$ of the total mural per day.
In 2 days, the work completed by A, B, and C together is:
$2\times \frac{5}{16}=\frac{10}{16}=\frac{5}{8}$

Step 3: Calculate the remaining work.
Subtract the work completed in the first 2 days from the total work:
$1-\frac{5}{8}=\frac{3}{8}$
Thus, $\frac{3}{8}$ of the mural remains to be completed.

Step 4: Determine the new working rates for B and C.
After 2 days, A leaves. B and C continue working, but only for $\frac{1}{2}$ of their usual daily working time. This reduces their daily rate by half:
New daily rate of B = $\frac{1}{2}\times \frac{1}{16}=\frac{1}{32}$
New daily rate of C = $\frac{1}{2}\times \frac{1}{20}=\frac{1}{40}$
The combined new daily rate of B and C is:
$\frac{1}{32}+\frac{1}{40}$
The LCM of 32 and 40 is 160:
$\frac{5+4}{160}=\frac{9}{160}$

Step 5: Calculate the additional days required to finish the remaining work.
Let $d$ be the number of additional days needed.
$d\times \frac{9}{160}=\frac{3}{8}$
Solving for $d$:
$d=\frac{3}{8}÷\frac{9}{160}$
$d=\frac{3}{8}\times \frac{160}{9}$
$d=\frac{3\times 160}{8\times 9}=\frac{20}{3}=6\frac{2}{3}$

Therefore, B and C will need an additional $6\frac{2}{3}$ days to complete the mural.