A and B can complete a work alone in 15 days and 25 days, respectively. They start together, but B leaves after some time and A finishes the remaining work in the last 7 days. After how many days from the start did B leave?

Introduction / Context:When one worker leaves before completion, split the work into two phases: joint phase and solo phase. Use rates to form an equation for the total work.

Given Data / Assumptions:

• A = 1/15 per day; B = 1/25 per day.
• A alone finishes the last 7 days.
• Let x = days they worked together.

Concept / Approach:Work done = x*(A+B) + 7*A = 1. Solve for x.

Step-by-Step Solution:

Verification / Alternative check:Check totals: 5*(8/75) = 8/15; plus 7/15 = 1 → consistent.

Why Other Options Are Wrong:They do not satisfy the total-work equation when rates are used correctly.

Common Pitfalls:Equating times instead of work; arithmetic slips when converting to common denominators.

Final Answer:5