Staggered team with A quitting early: A, B, and C can complete a work individually in 8, 12, and 15 days, respectively. A and B start together; after working for 2 days, A quits. Then C joins B and they continue till completion. In how many days (total) is the work finished?

Introduction / Context:
Split the timeline: first 2 days with A + B, then B + C for the remainder. Convert all times to per-day rates, compute fractions done, and sum durations.

Given Data / Assumptions:

• A = 1/8 per day.
• B = 1/12 per day.
• C = 1/15 per day.
• Days 1–2: A + B; thereafter: B + C.

Concept / Approach:
Work done first 2 days = 2 * (A + B). Remaining = 1 − that. Time to finish remainder = remaining / (B + C).

Step-by-Step Solution:
A + B = 1/8 + 1/12 = (3 + 2)/24 = 5/24.Work in 2 days = 2 * 5/24 = 10/24 = 5/12.Remaining = 1 − 5/12 = 7/12.B + C = 1/12 + 1/15 = (5 + 4)/60 = 9/60 = 3/20.Time for remainder = (7/12) / (3/20) = (7/12) * (20/3) = 35/9 days.Total time = 2 + 35/9 = 53/9 days.

Verification / Alternative check:
Approximation: 53/9 ≈ 5.888…, plausible since after an initial push, two moderate workers finish.

Why Other Options Are Wrong:
The other fractions do not equal 2 + (7/12)/(3/20) and thus misrepresent the segmented rates.

Common Pitfalls:
Adding times instead of rates; forgetting that A leaves after exactly 2 days.

Final Answer:
53/9 days