After initial teamwork, B completes the remainder: A and B together complete a job in 24 days. A alone can complete it in 32 days. Both work together for 8 days and then A leaves. How many days will B take to finish the remaining work?

Introduction / Context:
Use A’s solo time and the joint time to infer B’s rate, then apply it to the remaining fraction after the initial collaboration.

Given Data / Assumptions:

• A + B = 1/24 per day.
• A = 1/32 per day ⇒ B = 1/24 − 1/32 = 1/96 per day.
• First 8 days: both together.

Concept / Approach:
Compute initial completed portion, then divide the remainder by B’s rate.

Step-by-Step Solution:
Work in first 8 days = 8 * (1/24) = 1/3.Remaining work = 1 − 1/3 = 2/3.B alone time = (2/3) / (1/96) = 64 days.

Verification / Alternative check:
Rough check: B is slow (96 days alone), so 2/3 of the job indeed needs about 64 days.

Why Other Options Are Wrong:
16, 32, 48, and 40 days misapply either the initial 8-day contribution or B’s rate.

Common Pitfalls:
Subtracting times rather than rates; ignoring that only 1/3 was done initially.

Final Answer:
64 days