A can complete a project in 10 days and B can complete the same project in 15 days. A and B start working on the project together and A quit 5 days before the project is completed. In how many days is the project completed?

Explanation

Given: A can complete a project in 10 days and B can complete the same project in 15 days. A and B start working on the project together and A quit 5 days before the project is completed. Concept used: Total work = Efficiency (Work done per hour) × Total time taken Calculation: LCM (10, 15) = 30 Let the total project be the LCM of the time taken by different workers. So, total project = 30 units A's efficiency = 30/10 = 3 unit per day B's efficiency = 30/15 = 2 unit per day Let in N days the project be completed. According to the question, 3 × (N - 5) + 2 × N = 30 ⇒ 3N - 15 + 2N = 30 ⇒ 5N = 15 + 30 ⇒ N = 45/5 ⇒N=9 ∴ The project is completed in 9 days.