A takes three times as long as B and C together to do a job. B takes four times as long as A and C together to do the work. If all the three, working together can complete the job in 24 days, then the number of days. A alone will take to finish the job is

The correct option is 96.

Let us solve the problem step-by-step by defining the rate of work done by A, B, and C per day.

Let the work done by A, B, and C in one day be represented by $A$, $B$, and $C$ respectively.

According to the problem, A takes three times as long as B and C together to do the job. Since the time taken is inversely proportional to the rate of work, A's daily work is $\frac{1}{3}$ of the work done by B and C together daily.
This can be written as:
$A=\frac{1}{3}(B+C)$

From this relation, we can express $B+C$ in terms of $A$:
$B+C=3A$

We are given that all three working together can complete the job in 24 days. Therefore, the total work done by A, B, and C together in one day is:
$A+B+C=\frac{1}{24}$

Now, substitute the value $B+C=3A$ into the equation representing their combined daily work:
$A+3A=\frac{1}{24}$

Simplify the equation to find the value of $A$:
$4A=\frac{1}{24}$
$A=\frac{1}{24\times 4}$
$A=\frac{1}{96}$

Since A does $\frac{1}{96}$ of the work in one day, A alone will take 96 days to finish the entire job.