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1. 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

Solution:

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)

\begin{aligned} ∴ (\frac{360}{x} + 4) : \frac{360}{x} :: x : (x - 1) \\ \Leftrightarrow (\frac{360}{x} + 4) (x - 1) = \frac{360}{x} \times x \\ \Leftrightarrow 360 - \frac{360}{x} + 4 x - 4 = 360 \\ \Leftrightarrow 4 x - \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 \end{aligned}

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