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A contractor estimates that he can have the building construction completed in $40$ days by employing $15$ workers. After $12$ days of work, the work is paused for a week since he runs out of the building materials. How many workers must he add so that the building construction can be completed in time?
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Jay Patel

$15$ workers can do the work in $40$ days.

Assume, $15$ workers worked for $12$ days, then work is paused for a week, then $x$ workers worked for remaining $(40-12-7)$ days and completed the work.

Then,
$15×40=15×12+(40-12-7)x\\\Rightarrow 420=21x\\\Rightarrow x=20$

Number of workers he should add $=20-15=5$

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