According to the question,

In 1 day,

(B+C) together can complete $\frac{1}{8}$^th of the work     ...(1)

(A+B) together can complete $\frac{1}{12}$^th of the work   ...(2)

(A+C) together can complete $\frac{1}{16}$^th of the work   ...(3)

On adding equations 1, 2 and 3, we get 2(A+B+C)'s 1 day work

$$\begin{gathered} =\frac{1}{8}+\frac{1}{12}+\frac{1}{16} \\ =\frac{6+4+3}{48}=\frac{13}{48} \end{gathered}$$

⇒ (A+B+C)'s 1 days work$=\frac{13}{48\times 2}=\frac{13}{96}$

∴ A, B and C together can complete the work in $\frac{96}{13}$$or 7\frac{5}{13} days$

Hence option B is the correct.