Given Information:
A can complete the work individually in 8 days.
B can complete the work individually in 10 days.
C can complete the work individually in 15 days.

Approach:
To solve this problem, we will first calculate the individual rates of work for A, B, and C. Then we will determine the work done by A and B together in 2 days. Finally, we will calculate the time taken by B and C together to complete the remaining work.

Calculating Individual Rates of Work:
Let's calculate the individual rates of work for A, B, and C based on the given information:
A's rate of work = 1/8 (1 job in 8 days)
B's rate of work = 1/10 (1 job in 10 days)
C's rate of work = 1/15 (1 job in 15 days)

Work Done by A and B in 2 days:
Since A worked for 2 days and B worked for the entire duration, let's calculate the work done by A and B together in 2 days:
Work done by A and B together in 1 day = A's rate of work + B's rate of work
= 1/8 + 1/10
= 9/40 (work done in 1 day)
Work done by A and B together in 2 days = 2 * (9/40)
= 9/20

Remaining Work:
The remaining work after A and B quit is 1 - (9/20) = 11/20.

Time taken by B and C to complete the remaining work:
Since B and C are working together, their combined rate of work is:
B and C's combined rate of work = B's rate of work + C's rate of work
= 1/10 + 1/15
= 1/6 (work done in 1 day)
Time taken by B and C to complete the remaining work = (11/20) / (1/6)
= (11/20) * (6/1)
= 11/10
= 1.1 days

Total Time to Complete the Work:
The total time taken to complete the work is the sum of the time taken by A and B (2 days) and the time taken by B and C (1.1 days):
Total time to complete the work = 2 + 1.1
= 3.1 days

Therefore, the work will be completed in 3.1 days.

I think it's 27