Question

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 will they take to complete the job according to the new planning?

• A. 8 days
• B. 9 days
• C. 10 days
• D. 12 days

Hint:

For work problems, use the equation \( \text{Rate} \times \text{Time} = \text{Total Work} \) and compare scenarios.

Answer 1

The Correct Option is B

Let the number of days planned initially to complete the 360 articles be \( N \). Therefore, the number of articles to be made per day originally is \( \frac{360}{N} \). With the new plan, they make 4 more articles per day, so the new number of articles made per day is \( \frac{360}{N} + 4 \). According to the given condition, with the new plan, they will complete the job one day earlier, so the time taken in the new plan is \( N - 1 \). Thus, we can set up the following equation: \[ \frac{360}{N} \times N = \frac{360}{N + 4} \times (N - 1) \] Simplifying the equation, we get: \[ \frac{360}{N} = \frac{360}{N + 4} \quad \text{so,} \quad N = 36. \] Therefore, they will complete the job in 9 days (i.e., \( N - 1 \)).