Time and Work – Three workers with staggered start: Kareena can complete the entire work in 9 days, while Krishna alone needs 18 days. They both start together and work for the first 3 days. After that, Shahid joins them; he can finish the whole work alone in 3 days. Calculate the total number of days required for the three of them to complete the work under this schedule.

Introduction / Context:
Problems on time and work often use the idea that “work rate adds” when people work together. We convert each worker’s time to a daily rate and sum appropriately over the intervals when teams change.

Given Data / Assumptions:

• Kareena alone: 9 days ⇒ rate = 1/9 work/day.
• Krishna alone: 18 days ⇒ rate = 1/18 work/day.
• Shahid alone: 3 days ⇒ rate = 1/3 work/day.
• First 3 days: only Kareena + Krishna. After that: all three together, until completion.

Concept / Approach:
Their rates add when working together. Compute work done in the first segment, then finish the remainder with the larger team.

Step-by-Step Solution:
Combined rate of Kareena + Krishna = 1/9 + 1/18 = 1/6.Work done in first 3 days = 3 * (1/6) = 1/2.Remaining work = 1 - 1/2 = 1/2.All three together: 1/9 + 1/18 + 1/3 = 1/2 work/day.Time to finish remaining 1/2 at 1/2 per day = 1 day.Total time = 3 + 1 = 4 days.

Verification / Alternative check:
If the team of three does half the job in exactly one day, the arithmetic is internally consistent since their sum rate is 1/2.

Why Other Options Are Wrong:
6, 5, 7, and 8 days ignore either the strong boost from Shahid’s rate or mis-compute the first 3-day segment.

Common Pitfalls:
Forgetting to split the timeline at the 3-day mark; adding times instead of rates; or using 3 days of all three workers from the start.

Final Answer:
4 days