A and B can together finish a work in 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the job ? (S.S.C., 2003)

### Concept & Remaining Work Proportion Calculate the fraction of the job completed by the team before someone leaves. The remaining fraction is proportional to the time it takes the solo worker to finish it, allowing you to scale up to their time for the full job. ### Step-by-Step Solution * **Given:** A and B together can finish a work in 30 days. They work for 20 days. A finishes the remaining work in 20 days. * **Calculation:** The combined 1-day work of (A + B) is $1/30$. * They work together for 20 days. * Work completed = $20 \times (1/30) = 20/30 = 2/3$. * Determine the fraction of work left. * Remaining work = $1 - 2/3 = 1/3$. * We are given that A alone finishes this remaining $1/3$ of the work in 20 days. * If A takes 20 days to do $1/3$ of the work, the time A would take to do 1 entire job (the whole work) is $20 \times 3 = 60$ days. ### Exam Strategy & Shortcut If A+B take 30 days, working 20 days means they finished $2/3$ of the job. Only $1/3$ remains. Since A takes 20 days to do this $1/3$, A will take $20 \times 3 = 60$ days to do the whole $3/3$ of the job. ### Common Pitfall A common mistake is finding the remaining work ($1/3$) and incorrectly dividing 20 by $1/3$ or setting up an inverse proportion, leading to calculating B's efficiency instead of A's. ### Final Answer Therefore, the correct answer is **60**.