A and B working together can do a piece of work in 6 days. B alone can do the same work in 12 days. How long (in days) will A alone take to do double the work?

The correct option is 24.

Step 1: Determine the total work rate of A and B together.
A and B together can complete a piece of work in 6 days.
Therefore, the fraction of work completed by (A + B) in 1 day is:

$\text{Work done by (A + B) in 1 day}=\frac{1}{6}$

Step 2: Determine the work rate of B alone.
B alone can complete the same work in 12 days.
Therefore, the fraction of work completed by B in 1 day is:

$\text{Work done by B in 1 day}=\frac{1}{12}$

Step 3: Calculate the work rate of A alone.
Subtract B's 1-day work rate from the combined 1-day work rate of (A + B):

$\text{Work done by A in 1 day}=\frac{1}{6}-\frac{1}{12}$

Taking the least common multiple (LCM) of 6 and 12, which is 12:

$\text{Work done by A in 1 day}=\frac{2-1}{12}=\frac{1}{12}$

Step 4: Find the time taken by A to complete the single work.
Since A completes $\frac{1}{12}$ of the work in 1 day, A alone takes 12 days to complete 1 unit of work.

Step 5: Calculate the time taken by A to complete double the work.
To do double (2 times) the amount of work, A will take twice as long:

$\text{Time required for double work}=12\times 2=24\text{days}$

Thus, A alone will take 24 days to complete double the work.