Question

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?

Answer 1

The basic formula is r * w * t = q 

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%. 

The number of workers must be increased by 28%.