A can do a piece of work in 15 days, which B can do in 10 days. B worked at it for 8 days. A can finish the remaining work in (R.R.B., 2004)

### Concept & Remaining Work Calculation When one person partially completes a job and leaves, determine the exact fraction of the work they accomplished. The remaining fraction is then multiplied by the total time the second person would need to complete the entire job alone. ### Step-by-Step Solution * **Given:** A finishes in 15 days, B finishes in 10 days. B works alone for 8 days. * **Calculation:** Calculate B's 1-day work. * B's 1-day work = $1/10$. * B works for 8 days. Work done by B = $8 \times (1/10) = 8/10 = 4/5$. * Determine the remaining work to be done by A. * Remaining work = $1 - 4/5 = 1/5$. * We know A can do 1 complete job (the whole work) in 15 days. * Time taken by A to finish the remaining $1/5$ of the work = $(1/5) \times 15$ days. * Time = 3 days. ### Exam Strategy & Shortcut Using the LCM method for speed: Let Total Work = LCM(15, 10) = 30 units. Efficiency of A = $30/15 = 2$ units/day. Efficiency of B = $30/10 = 3$ units/day. B worked for 8 days, doing $8 \times 3 = 24$ units. Remaining work = $30 - 24 = 6$ units. Time A needs to finish 6 units = Remaining Work / A's Efficiency = $6 / 2 = 3$ days. ### Common Pitfall A classic error is calculating the remaining work accurately but then dividing it by A's one-day work improperly, or mistakenly applying B's efficiency to A's remaining calculation timeline. Keep track of whose efficiency belongs to whom. ### Final Answer Therefore, the correct answer is **3 days**.