Three People Working Together A can do a job in 8 days, B can do it in 16 days, and C can do it in 80 days. If all three work together, how many days are needed to complete the work?

Introduction / Context:
This is a straightforward combined-rate problem involving three workers. Convert each to a rate, add them, and invert to get the total time. Such questions appear frequently in aptitude tests.

Given Data / Assumptions:

• A: 8 days ⇒ 1/8 per day.
• B: 16 days ⇒ 1/16 per day.
• C: 80 days ⇒ 1/80 per day.

Concept / Approach:
Combined rate r = 1/8 + 1/16 + 1/80. Time = 1/r. Use a common denominator to avoid errors.

Step-by-Step Solution:
Common denominator 80: 1/8 = 10/80, 1/16 = 5/80, 1/80 = 1/80.r = (10 + 5 + 1)/80 = 16/80 = 1/5 job/day.Time = 1 / (1/5) = 5 days.

Verification / Alternative check:
Average speed logic confirms that adding even a slow helper (C) still improves total rate modestly, not dramatically.

Why Other Options Are Wrong:
6 or more days imply a rate slower than 1/5; 8 2/3 and 20 2/5 are far off; 4 days would require a faster combined rate than available.

Common Pitfalls:
Adding times instead of rates or omitting the contribution of the slowest worker altogether.

Final Answer:
5