SOLUTION: The volume of construction work was increased by 60% but the productivity of labor increased by only 25% By wha percent must the workers be increased?

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Question 1033403: The volume of construction work was increased by 60% but the productivity of labor increased by only 25% By wha percent must the workers be increased?
Answer by ikleyn(52818) About Me  (Show Source):
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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%28the_number_of%29 the workers be increased?
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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 = %281.6V+-+1.25%2Ar%2AN%29%2F%281.25%2Ar%2AN%29 = %281.6%2AV%29%2F%281.25%2Ar%2AN%29+-+1 = 1.6%2F1.25+-+1 = 1.28 - 1 = 0.28.

Answer.  The number of workers must be increased by 28%.