A can finish a job in 10 days and B in 20 days. They start together, but A leaves 2 days before completion. In how many days is the whole job finished?

Introduction / Context:
Staggered participation requires expressing total work as the sum of contributions over the exact durations each worker is present. Create an equation in terms of the unknown total time and solve.

Given Data / Assumptions:

• A: 10 days ⇒ 1/10 per day.
• B: 20 days ⇒ 1/20 per day.
• A works until 2 days before the end; B works the entire duration.

Concept / Approach:
Let total time be T days. Then A works T − 2 days and B works T days. Set total work to 1 and solve for T.

Step-by-Step Solution:

Verification / Alternative check:
Check contributions: A works 6 days at 1/10 = 0.6; B works 8 days at 1/20 = 0.4; total is 1 job.

Why Other Options Are Wrong:
7 2/3, 7, 6, 9 days fail the linear equation or give totals less or more than the full job.

Common Pitfalls:
Letting A also work the last 2 days; mixing time and rate averages; arithmetic mistakes solving the linear equation.

Final Answer:
8 days