A and B can complete a work in 15 and 10 days respectively. They work together for 2 days, then B leaves and A completes the rest. In how many total days is the work finished?

Problem restatementTwo workers start together; one leaves after 2 days. Find total completion time.

Given data

• A: 15 days ⇒ 1÷15 per day
• B: 10 days ⇒ 1÷10 per day
• Together for first 2 days

Concept/ApproachCompute the fraction completed in the first 2 days, then let A finish the remainder.

Step-by-step calculationWork in first 2 days = 2 × (1÷15 + 1÷10) = 2 × (1÷6) = 1÷3Remaining work = 1 − 1÷3 = 2÷3A alone time = (2÷3) ÷ (1÷15) = (2÷3) × 15 = 10 daysTotal time = 2 + 10 = 12 days

Verification/AlternativeDaily accounting confirms the fractions.

Common pitfallsDo not distribute the 2 days equally as 1 each without computing rates.

Final Answer12 days