Back-infer B’s solo time from a shortfall scenario: A and B together can complete a work in 3 days. They start together, but after 2 days B leaves. The work finishes 2 days later (i.e., after 4 days total). How many days would B alone take to complete the work?

Introduction / Context:
We know the pair’s rate and the actual timeline with B leaving. Express total work as the sum of two segments and solve for A’s rate first, then B’s time.

Given Data / Assumptions:

• A + B = 1/3 per day.
• First 2 days: both work; last 2 days: A alone; total = full job.

Concept / Approach:
Compute: 2*(A + B) + 2*A = 1 ⇒ isolate A, then get B = 1/3 − A.

Step-by-Step Solution:
2*(1/3) + 2a = 1 ⇒ 2/3 + 2a = 1 ⇒ 2a = 1/3 ⇒ a = 1/6.Then b = 1/3 − 1/6 = 1/6.B alone time = 1 / (1/6) = 6 days.

Verification / Alternative check:
Check total: 2*(1/3) + 2*(1/6) = 2/3 + 1/3 = 1 ✔.

Why Other Options Are Wrong:
5, 7, 8, and 10 days do not match the deduced rate for B.

Common Pitfalls:
Assuming both have the same time from the start without solving; or misreading “2 more days”.

Final Answer:
6 days