Rashmi can complete a work in 16 days, Ravina in 12 4/5 (12.8) days, and Gitika in 32 days. They start together; Rashmi leaves after 4 days, and Ravina leaves 3 days before completion. How long does the work take in total?

Introduction / Context:
Another staged-contribution problem: all three begin, then Rashmi leaves early and, later, Ravina leaves before the end. Sum contributions over the appropriate intervals to solve for total time T.

Given Data / Assumptions:

• Rashmi (R) = 1/16 per day; Ravina (V) = 1/12.8 = 5/64 per day; Gitika (G) = 1/32 per day.
• All three work for the first 4 days; then only V and G until the last 3 days; finally only G for the last 3 days.

Concept / Approach:
Partition the timeline into three intervals and add their contributions. Let T be total days. Middle interval length is (T - 7) days.

Step-by-Step Solution:

Verification / Alternative check:
Rough bounds: With three workers at start then fewer later, 9 days is plausible between the fastest joint and single-worker extremes.

Why Other Options Are Wrong:
They do not satisfy the partitioned-rate equality.

Common Pitfalls:
Misinterpreting “3 days before completion” as an isolated day rather than the last 3-day block without Ravina.

Final Answer:
9 days