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 %

Step-by-step 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,

$\frac{1}{1.6} = \frac{x}{1.25y}$

$1.25 y = 1.6 x$

$y = \frac{1.6x}{1.25}$

$y = \frac{160x}{125}$

Thus, the percentage increase in the number of workers = $\frac{160x/125-x}{x}\times 100$

$\frac{160x-125x}{125x}\times 100$

$\frac{35x}{125x}\times 100$

$\frac{35}{125}\times 100$

$\frac{3500}{125}$

$28\%$

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

Answer 2

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

Step-by-step 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

$v=p\times n$

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,

$\frac{100+60}{100}\times v=\frac{100+25}{100}\times p\times n(1+x)\\\\1.6\times v=1.25\times p\times n(1+x)\\\\1.6\times p\times n=1.25\times p\times n(1+x)\\\\\frac{1.6}{1.25}=1+x\\\\1.28=1+x\\\\1.28-1=x\\\\x=0.28$

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