Staggered Collaboration — B Joins After 10 Days A can complete a job in 25 days and B can complete it in 20 days. A starts alone and B joins after 10 days. What is the total duration of the work (in days)?

Introduction / Context:
Another phased-work problem: one person starts, the second joins later. Compute the work done initially, then finish the rest at the combined rate. Convert fractional days to mixed fractions at the end for clarity.

Given Data / Assumptions:

• A alone: 25 days ⇒ rate = 1/25.
• B alone: 20 days ⇒ rate = 1/20.
• A works alone for first 10 days.

Concept / Approach:
Work after 10 days by A is subtracted from the total. The remainder is completed at the combined rate (A + B).

Step-by-Step Solution:
Work by A in 10 days = 10*(1/25) = 2/5.Remaining = 1 − 2/5 = 3/5.Combined rate (A + B) = 1/25 + 1/20 = 9/100 per day.Time for remaining = (3/5) / (9/100) = (3/5)*(100/9) = 60/9 = 20/3 days = 6 2/3 days.Total time = 10 + 6 2/3 = 16 2/3 days.

Verification / Alternative check:
Decimal: 9/100 = 0.09 per day. Remaining 0.6/0.09 = 6.666... days, confirming the result.

Why Other Options Are Wrong:
Other durations do not satisfy the phased-rate arithmetic.

Common Pitfalls:
Adding times directly or treating B’s contribution as starting earlier than given.

Final Answer:
16 2/3 days