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: The number of number of workers is increased by 28%.

Explanation:

Let the volume of construction work be v

Let the productivity of labor be p.

Let the number of workers be n.

So, our original equation becomes

`v=p* n`

Now,

According to question, we have given that if volume increased by 60% and the productivity increases by 25%.

Let the percentage increase in number of workers be x

So, it becomes,

`(100+60)/(100)* v=(100+25)/(100)* p* n(1+x)\\\\1.6* v=1.25* p* n(1+x)\\\\1.6* p* n=1.25* p* n(1+x)\\\\(1.6)/(1.25)=1+x\\\\1.28=1+x\\\\1.28-1=x\\\\x=0.28`

So, The number of number of workers is increased by 28%.

Answer 2

Answer: 28 %

Explanation:

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

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

Then, V = p × N × x ------ (1)

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

Let y be the new number of workers,

Then, 1.6 V = 1.25 p × N × y -------(2)

Dividing equation (1) by equation (2)

We get,

`(1)/(1.6) = (x)/(1.25y)`

`1.25 y = 1.6 x`

`y = (1.6x)/(1.25)`

`y = (160x)/(125)`

Thus, the percentage increase in the number of workers =
`(160x/125-x)/(x)* 100`

`(160x-125x)/(125x)* 100`

`(35x)/(125x)* 100`

`(35)/(125)* 100`

`(3500)/(125)`

`28\%`

Therefore, the number of workers is increased by 28%.