A team of workers was employed by a contractor who undertook to finish 360 pieces of an article in a certain number of days. Making four more pieces per day than was planned, they could complete the job a day ahead of schedule. How many days did they take to complete the job?

### Concept & Rate of Work This problem connects total work, rate of work, and time taken. $$ \text{Total Work} = \text{Rate} \times \text{Time} $$ If the total work is constant, an increase in the rate results in a decrease in time. ### Step-by-Step Solution * **Variables:** Let the originally planned number of days be $x$. The total pieces to be made is 360. * **Planned Rate:** The planned number of pieces per day is $\frac{360}{x}$. * **Actual Scenario:** They made 4 more pieces per day, so the actual rate is $\frac{360}{x} + 4$. They finished a day ahead of schedule, so the actual time taken is $x - 1$ days. * **Equation:** The total work is the product of actual rate and actual time. * $(\frac{360}{x} + 4)(x - 1) = 360$ * $360 - \frac{360}{x} + 4x - 4 = 360$ * $4x - \frac{360}{x} - 4 = 0$ * Divide by 4: $x - \frac{90}{x} - 1 = 0$ * Multiply by $x$: $x^2 - x - 90 = 0$ * **Factorize:** $(x - 10)(x + 9) = 0$. Since days cannot be negative, $x = 10$. * **Final Step:** The planned number of days was 10. The question asks how many days they *did* take (actual time), which is $10 - 1 = 9$ days. ### Exam Strategy & Shortcut Use option elimination on the actual days taken. If actual days = 9 (Option B), then planned days = 10. Planned rate = $360 / 10 = 36$. Actual rate = $360 / 9 = 40$. Difference in rate = $40 - 36 = 4$. This matches the condition "four more pieces per day". Option B is correct. ### Common Pitfall A major pitfall is solving the quadratic equation for $x$ (which gives 10) and selecting 10 as the answer, forgetting that $x$ is the *planned* time, but the question asks for the *actual* time taken ($x - 1$). ### Final Answer Therefore, the correct answer is **9 days**.