Time and Work – Staggered departures: Kavita, Babita, and Samita start a job together. Samita leaves after the first 5 days, and Babita leaves after completing 8 days of work in total. Individually, their times to finish the entire work alone are: Kavita 20 days, Babita 60 days, and Samita 30 days. After these departures, in how many additional days will Kavita alone complete the remaining work?

Introduction / Context:
When workers enter or leave at different times, break the timeline into segments and add rates within each segment to track cumulative work completed.

Given Data / Assumptions:

• Kavita: 20 days ⇒ rate = 1/20 per day.
• Babita: 60 days ⇒ rate = 1/60 per day.
• Samita: 30 days ⇒ rate = 1/30 per day.
• Days 1–5: all three; days 6–8: Kavita + Babita; after day 8: Kavita alone.

Concept / Approach:
Compute work done in each phase and subtract from 1 to find the remainder for Kavita alone.

Step-by-Step Solution:
All three rate = 1/20 + 1/60 + 1/30 = 1/10.Work in first 5 days = 5 * 1/10 = 1/2.Next 3 days (Kavita + Babita): rate = 1/20 + 1/60 = 1/15 ⇒ work = 3 * 1/15 = 1/5.Total done by day 8 = 1/2 + 1/5 = 7/10.Remaining = 1 - 7/10 = 3/10.Kavita alone: time = (3/10) / (1/20) = 6 days.

Verification / Alternative check:
Convert to a 60-unit job: first phase 30 units, second 12 units; 18 units remain at 3 units/day ⇒ 6 days.

Why Other Options Are Wrong:
4, 5, 7, and 8 days mis-calc the split or Kavita’s solo rate for the remainder.

Common Pitfalls:
Not isolating the 5-day and 3-day segments; arithmetic slips in adding fractional rates.

Final Answer:
6 days