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?
(a)8 days
(b)9 days
(c)10 days
(d)12 days
Answer
Answer (as printed): C
Explanation
Let the team take $x$ days to finish 360 pieces. Then, number of pieces made each day $= \frac{360}{x}$. More number of pieces per day, Less days (Indirect Proportion). $\left(\frac{360}{x}+4\right) : \frac{360}{x} :: x : (x-1)$. $\Leftrightarrow \left(\frac{360}{x}+4\right)(x-1) = \frac{360}{x} \times x = 360 \Leftrightarrow 360 - \frac{360}{x} + 4x - 4 = 360 \Leftrightarrow 4x - \frac{360}{x} - 4 = 0 \Leftrightarrow x - \frac{90}{x} - 1 = 0 \Leftrightarrow x^{2} - x - 90 = 0 \Leftrightarrow (x-10)(x+9) = 0 \Leftrightarrow x = 10$.
Explanation as extracted from the printed page; notation may be imperfect.