A man completes $\frac{5}{8}$ of a job in 10 days. At this rate, how many more days will it take him to finish the job? (M.B.A., 2003)

### Concept & Unitary Method for Work When a fraction of work is tied to a specific time, you can determine the time for a single "unit" or "part" of the work and scale it to the remaining parts. $$ \text{Time for Remaining Work} = \text{Remaining Fraction} \times \text{Total Time for 1 Job} $$ ### Step-by-Step Solution * Given: The man completes 5 parts out of 8 total parts ($\frac{5}{8}$) in 10 days. * Time taken for 1 part of the job = $\frac{10}{5} = 2$ days. * Remaining parts of the job to be completed = $8 - 5 = 3$ parts (or $\frac{3}{8}$ of the job). * Time taken for remaining 3 parts = $3 \times 2 = 6$ days. ### Exam Strategy & Shortcut Set up a direct proportion between work parts and days: $5 \text{ parts} \rightarrow 10 \text{ days}$ $1 \text{ part} \rightarrow 2 \text{ days}$ $3 \text{ parts} \rightarrow 6 \text{ days}$. The answer is 6 immediately. ### Common Pitfall Calculating the total number of days required to finish the *entire* job (16 days) instead of reading carefully that the question asks for how many *more* days it will take. ### Final Answer Therefore, the correct answer is **6**.