A and B together can do a work in 12 days, whereas B and C can do it in 24 days. If A, B, and C collectively can finish the same work in 8 days, then how many days will it take for A and C together to finish it?

The correct option is D 8 days
A and B together can finish a work in 12 days.

$\text{(A + B)'s one day work}=\frac{1}{12}$ -------(1)

B and C together can finish the same work in 24 days.

$\text{(B + C)'s one day work}=\frac{1}{24}$ -------(2)

Also, given that A, B, and C together can finish the work in 8 days.

$\text{(A + B + C)'s one day work}=\frac{1}{8}$ ---(3)

Subtract (1) from (3), to get C's one day work

$⟹(A+B+C)-(A+B)=\frac{1}{8}-\frac{1}{12}$

$⟹\text{C's one day's work}=\frac{1}{8}-\frac{1}{12}$

$⟹\text{C's one day's work}=\frac{3-2}{24}$

$⟹C=\frac{1}{24}$

Subtract (2) from (3), to get A's one day work

$⟹(A+B+C)-(B+C)=\frac{1}{8}-\frac{1}{24}$

$⟹\text{A's one day's work}=\frac{1}{8}-\frac{1}{24}$

$⟹\text{A's one day's work}=\frac{3-1}{24}$

$⟹\text{A's one day's work}=\frac{2}{24}$

$⟹\text{A's one day's work}=\frac{1}{12}$

Now let's find A and C work together.

$\text{(A+C)'s one day's work}=\frac{1}{24}+\frac{1}{12}$

$\text{(A+C)'s one day's work}=\frac{1+2}{24}$

$\text{(A+C)'s one day's work}=\frac{3}{24}$

$\text{(A+C)'s one day's work}=\frac{1}{8}$

Therefore, the number of days in which A and C can finish the work will be 8 days.