A and B can complete a work together in 30 days. They work together for 20 days; then B leaves, and A finishes the remaining work in the next 20 days. In how many days can A alone finish the work?

Problem restatementThe pair completes a project in 30 days. After 20 days of working together, B leaves; A alone completes the rest in 20 days. Find A's solo time.

Given data

• (A + B) time = 30 days ⇒ (A + B) rate = 1÷30 per day.
• First phase: 20 days together.
• Second phase: 20 days by A alone.

Concept/ApproachCompute the fraction completed in phase 1; the remainder is done by A in phase 2, which gives A's rate.

Step-by-step calculationWork done in first 20 days = 20 × (1÷30) = 2÷3Remaining work = 1 − 2÷3 = 1÷3A completes 1÷3 in 20 days ⇒ A's rate = (1÷3) ÷ 20 = 1÷60 per dayTherefore, A's time alone = 60 days

Verification/AlternativeCheck units: rate in job/day times days gives fraction of job, consistent in both phases.

Common pitfallsForgetting that only A works in the last 20 days; mixing average of 30 and 20 without using rates is incorrect.

Final Answer60 days