To find out the time taken by B to complete (7/9)th of the original work alone, we need to follow the given information and solve step by step.

Given Information:
- A completes the task in 24 days.
- The task is completed in 11(1/3) days with A and B working on alternate days, starting with B.

Let's break down the problem into smaller parts and solve it step by step.

Step 1: Find the work done by A and B together in one day
- A takes 24 days to complete the task, so A's 1 day work = 1/24
- Let's assume B's 1 day work = x (to find x)

Step 2: Find the work done by A and B in 11(1/3) days
- In 11(1/3) days, A and B work on alternate days, starting with B.
- In 11 days, B works for 6 days (as B starts on the first day)
- In 1/3 day, A works (as A works on alternate days)
- So, the total work done in 11(1/3) days = (6 * x) + (1/3 * 1/24)

Step 3: Find the remaining work after 11(1/3) days
- The task is completed in 11(1/3) days, so the remaining work = 1 - (work done in 11(1/3) days)

Step 4: Find the work done by B in one day
- As A and B work on alternate days, starting with B, B's work is done for 6 days in 11(1/3) days.
- So, B's 1 day work = (work done by B in 11(1/3) days) / 6

Step 5: Find the time taken by B to complete (7/9)th of the original work alone
- The remaining work after 11(1/3) days is (7/9)th of the original work.
- B's work alone is needed to complete this remaining work.
- So, the time taken by B to complete (7/9)th of the original work alone = (remaining work after 11(1/3) days) / (B's 1 day work)

Let's summarize the steps:

Step 1:
A's 1 day work = 1/24
B's 1 day work = x

Step 2:
Total work done in 11(1/3) days = (6 * x) + (1/3 * 1/24)

Step 3:
Remaining work = 1 - (work done in 11(1/3) days)

Step 4:
B's 1 day work = (work done by B in 11(1/3) days) / 6

Step 5:
Time taken by B to complete (7/9)th of the original work alone = (remaining work) / (B's 1 day work)

By following these steps and substituting the values appropriately, you can calculate the time taken by B to complete (7/9)