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 restatement
Two 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/Approach
Compute the fraction completed in the first 2 days, then let A finish the remainder.

Step-by-step calculation
Work 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/Alternative
Daily accounting confirms the fractions.

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

Final Answer
12 days