A, b, c can complete a work separately in 24, 36, and 48 days respectively. They started working together but C left after 4 days of start and A left 3 days before the completion of the work. In how many days will the work be completed ?

in 4 days, A&B&C did

4(1/24 + 1/36 + 1/48) = 13/36 of the job

In the last 3 days, B working alone did 3/36 = 1/12 of the job

That left A&B to do 5/9 of the work

1/24 + 1/36 = 5/72, so it took A&B 8 days to do their part.

To find out how many days it will take to complete the work, we need to calculate the amount of work done by each person in one day.

Let's assume that the total work that needs to be done is represented by W.

We are given the following information:
- A can complete the work in 24 days. Therefore, in one day, A can complete 1/24th of the work.
- B can complete the work in 36 days. Therefore, in one day, B can complete 1/36th of the work.
- C can complete the work in 48 days. Therefore, in one day, C can complete 1/48th of the work.

In four days, A, B, and C would have completed the following amount of work:
- A: (1/24) * 4 = 1/6th of the work
- B: (1/36) * 4 = 1/9th of the work
- C: (1/48) * 4 = 1/12th of the work

So, in total, in four days, they have completed (1/6 + 1/9 + 1/12) of the work.

To find out how much work is left, we subtract this amount from the total work W:
Remaining work = W - (1/6 + 1/9 + 1/12) * W

Now, we know that A left 3 days before the completion of the work. So, the remaining work was being done by B and C.
Let's assume it takes X days for B and C to complete the remaining work.

In X days, B would have completed:
- (1/36) * X of the remaining work.

In X days, C would have completed:
- (1/48) * X of the remaining work.

Since we also know that in four days they completed 1/6th of the work, we can set up the following equation:
(1/6) = (1/36) * X + (1/48) * X

Simplifying this equation, we get:
(1/6) = (2/72) * X + (1/48) * X

Combining the fractions on the right side, we get:
(1/6) = (3/72) * X

Cross-multiplying, we get:
72 = 3X

Dividing both sides by 3, we get:
X = 24

Therefore, it will take B and C 24 days to complete the remaining work after A leaves.

Since A leaves 3 days before the completion of the work, the total number of days to complete the work is:
4 + 24 + 3 = 31 days.

So, the work will be completed in 31 days.