A does 50 percent of a certain piece of work in 12 days. He then calls in B and together they finish the remaining half of the work in 8 days. If the total work is considered as one complete job, how long would B alone take to complete the entire work?

Introduction / Context:
This time and work problem focuses on finding the individual efficiency of a second worker when the first worker does part of the job alone and then both workers finish the remaining part together. Such questions check the understanding of work rates and how to combine or separate them based on given stages of work completion.

Given Data / Assumptions:
- A completes 50 percent (one half) of the work in 12 days when working alone.
- The remaining 50 percent of the work is completed by A and B together in 8 days.
- Work rate of each person is constant throughout the process.
- Total work is assumed to be 1 unit (one complete job).

Concept / Approach:
We convert the information into daily work rates. First we find A's rate from the time he takes to complete half of the work. Then we determine the combined rate of A and B from the time they take to finish the remaining half. The rate of B alone is then obtained by subtracting A's rate from the combined rate. Finally we calculate how long B would take to complete the whole work alone using his individual rate.

Step-by-Step Solution:
Step 1: Let total work = 1 unit. A does half of the work (1/2) in 12 days. Step 2: A's daily rate = (1/2) / 12 = 1/24 of the work per day. Step 3: The remaining work is 1/2. A and B together finish this in 8 days. Step 4: Combined rate of A and B = (1/2) / 8 = 1/16 of the work per day. Step 5: B's rate = combined rate − A's rate = 1/16 − 1/24. Step 6: Compute 1/16 − 1/24 = (3 − 2) / 48 = 1/48 of the work per day. Step 7: Time taken by B alone to do the whole work = 1 / (1/48) = 48 days.

Verification / Alternative check:
Check consistency: If B works at 1/48 per day, then in 8 days B does 8 * 1/48 = 1/6 of the work. During those same 8 days A does 8 * 1/24 = 1/3 of the work. Together they complete 1/6 + 1/3 = 1/2 of the work in 8 days, which matches the statement that the remaining half is finished in 8 days. This confirms that the calculated rates are correct.

Why Other Options Are Wrong:
Option 12 days: This would mean B is much faster than A, which contradicts the fact that A already took 12 days just for half the work.
Option 24 days: This implies B is exactly as fast as A, but the combined time for the second half would then be shorter than the given 8 days.
Option 36 days: Also does not satisfy the given combined time condition; it leads to inconsistent fractions of work when rechecked.

Common Pitfalls:
Many learners forget to treat the work in fractions and try to add days directly. Another common error is to divide the remaining time incorrectly between the workers instead of computing their rates. Always convert to rates, subtract to find the unknown worker's rate, and then invert to get the time.

Final Answer:
B alone would take 48 days to complete the entire work.