The volume of construction work was increased by 60% but the productivity of labor increased by only 25%. By what percent must the number of workers be increased?
r = quantity of output produced per worker per unit of time. w = number of workers. t = time q = quantity of output produced.
you can solve this formula for w to get:
w = q / (r * t)
if the quantity of work increases by 60%, then you get 1.6 * q and the formula for w becomes:
w = (1.6 * q) / (r * t)
a 60% increase in the quantity of would result in a 60% increase in the number of workers required, assuming the amount of time available was the same.
not assume that each worker can produce 25% more output per unit time.
then you get 1.25 * r and the formula for w becomes:
w = (1.6 * q) / (1.25 * r * t)
this formula can also be written as (1.6/1.25) * (q/(r*t)).
this results in 1.28 * (q/(r*t)) which can also be written as (1.28 * q) / (r*t)
this says that the 60% increase in the quantity of work produced can be handled with a 28% increase in the number of workers required, assuming the amount of time available is the same, and assuming that the productivity of each worker has increased by 25%.
