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:

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,

$1.6 = 1.25\times \frac{n'}{n}$

$\frac{1}{1.6}=\frac{n}{1.25n'}$

$n' = \frac{1.6n}{1.25}$

Which is the new number of workers.

Thus, the percentage increase in the number of workers = $\frac{n'-n}{n}\times 100=\frac{1.6n/1.25-n}{n}\times 100 = \frac{1.6-1.25}{1.25}\times 100 = \frac{0.35}{1.25}\times 100 = 28\%$

⇒The number of workers is increased by 28%.