Staggered Start — One Worker Joins Later Mahesh and Umesh can complete a job in 10 days and 15 days, respectively. Umesh works alone for the first 5 days, after which Mahesh also joins. In how many total days is the work completed?

Introduction / Context:
When one worker starts and another joins later, split the timeline into phases and compute the partial work done in each phase using rates. Sum the completed parts to reach the full job.

Given Data / Assumptions:

• Mahesh alone: 10 days ⇒ rate = 1/10.
• Umesh alone: 15 days ⇒ rate = 1/15.
• Phase 1: Umesh works 5 days alone.
• Phase 2: Both work together afterward.

Concept / Approach:
Compute work done in Phase 1, subtract from 1, and finish the remainder using the combined rate.

Step-by-Step Solution:
Phase 1 work by Umesh = 5*(1/15) = 1/3.Remaining work = 1 − 1/3 = 2/3.Combined rate (Mahesh + Umesh) = 1/10 + 1/15 = 1/6 job/day.Time for remaining = (2/3) / (1/6) = (2/3)*6 = 4 days.Total time = 5 + 4 = 9 days.

Verification / Alternative check:
Daily contributions in Phase 2 sum to 1/6; in 4 days they complete 4/6 = 2/3, exactly what was left.

Why Other Options Are Wrong:
7, 8, 10, or 11 days do not match the phased rate calculation.

Common Pitfalls:
Adding times directly or forgetting to subtract the work already done in Phase 1 before computing Phase 2 duration.

Final Answer:
9 days