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:

Let, Initially,

V be the volume of construction work

r be the productivity of labor  

n be the number of days

x be the number workers.

Thus,  V  = r × n × x   ------------(1)      

Now, According to the question,

The volume of construction work was increased by 60% but the productivity of labor increased by only 25%.

Therefore,

Final volume of the work = 160% of V = 1.6 V

Final productivity = 125% of r = 1.25 r

Also, the time is same in both conditions,

Final time taken = n

Let y be the number of people after changes.

Thus, 1.6 V = 1.25 r × n × y -----(2)

Dividing equation (1) by equation (2)

We get, y = 1.60 x/1.25

Thus, the changes in the number of workers

= $\frac{(\frac{1.60x}{1.25}-x) }{x}\times 100$

= 0.28 × 100

= 28 %