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Question
A work-force of 420 men with a contractor can finish a certain piece of work in 9 months. How many extra men must he employ to complete the job in 7 months?
Solution
Let x be the extra number of men employed to complete the job in 7 months.
| Number of men | 420 | x |
| Months | 9 | 7 |
\[\text{ Since the number of men hired and the time required to finish the piece of work are in inverse variation, we have } : \]
\[420 \times 9 = 7x\]
\[ \Rightarrow x = \frac{420 \times 9}{7}\]
\[ = 540\]
\[\text{ Thus, the number of extra men required to complete the job in 7 months } = 540 - 420 = 120\]
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