Question 1033403
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The volume of construction work was increased by 60%, but the productivity of labor increased by only 25%.
By what percent must {{{highlight(the_number_of)}}} the workers be increased?
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<pre>
Let V be the original volume of construction work (the volume "before"),
    r be the productivity of labor "before", 
    N be the number of workers "before", and
    x be in what percent  the number of workers must be increased.

According to the condition, these quantities are constrained/connected by the equations

V     = r*N,                (1)      and 
1.6*V = 1.25r*N*(1+x).      (2)

From these equations,

x = {{{(1.6V - 1.25*r*N)/(1.25*r*N)}}} = {{{(1.6*V)/(1.25*r*N) - 1}}} = {{{1.6/1.25 - 1}}} = 1.28 - 1 = 0.28.

<U>Answer</U>.  The number of workers must be increased by 28%.
</pre>