The correct answer is option (E):
None of these
Let's analyze the problem.
A can complete a job in 24 days, meaning A's work rate is 1/24 of the job per day.
B can complete the same job in 26 days, meaning B's work rate is 1/26 of the job per day.
They work on alternative days, and B starts. This means the work progresses in cycles of two days: Day 1: B works, Day 2: A works.
Work done in a two-day cycle: B's work + A's work = (1/26) + (1/24) = (12 + 13) / (12*13) = 25/312
Now let's determine how many such cycles are needed. We need to find how many such two-day cycles are required to complete the work.
Let 'n' be the number of two-day cycles. In 'n' cycles, the amount of work done would be n * (25/312).
If we find 'n' such that the job is *just* completed, we would have n * (25/312) = 1 (complete job).
This implies n = 312/25 = 12.48 cycles. Which is not a complete cycle.
The process has to be continuous. So there will be 12 cycles completed in 24 days. After these 24 days,
The amount of work done is 12 * (25/312) = 300/312 = 25/26
Now, the remaining work = 1 - 25/26 = 1/26.
After 24 days, the next day, it will be B's turn to work. B can complete 1/26 of the work in one day. Which means the remaining work is completed in one day.
So we can also see this as 12 complete cycles (24 days) and 1 day with B working.
Hence the total number of days = 24 + 1 = 25 days.
However, consider this, we are given with only values with no decimals and fractions in the options.
If B completes the job in 26 days.
Work done by B = 1/26
Work done by A = 1/24
After 24 days.
Work done in two days (1/26+1/24) = 25/312
Total number of such cycles that can be completed.
Work done in each day =
Day 1: 1/26
Day 2: 1/24
If we divide the job.
The job can be completed in approximately 25 days with B starting the work.
So, the calculated answer is not among the options.
Therefore, the correct answer is 'None of these'.