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 in order for the work to be completed in time, as it was scheduled originally?

Answer 1

Answer: 28 %

Explanation:

Volume of a work = productivity × time × number of workers

Let V be the initial volume of the work , x is the initial productivity , n is the initial time and w be the initial number of workers.

Then, V = x × t × n ------ (1)

When, the volume of construction work was increased by 60%, productivity of labor increased by only 25% and time remains same,

Let w' be the new number of workers,

Then, 1.6 V = 1.25 x × t × n' -------(2)

After dividing equation (2) by equation (1),

We get,

`1.6 = 1.25* (n')/(n)`

`(1)/(1.6)=(n)/(1.25n')`

`n' = (1.6n)/(1.25)`

Which is the new number of workers.

Thus, the percentage increase in the number of workers =
`(n'-n)/(n)* 100=(1.6n/1.25-n)/(n)* 100 = (1.6-1.25)/(1.25)* 100 = (0.35)/(1.25)* 100 = 28\%`

⇒The number of workers is increased by 28%.