Question

ANSWER ASAP: New machine has productivity (measured in the number of produced details) 12% greater than the last model. After replacing the machines during renovation, a plant has 5% fewer new models than it had old models before. By what percent did the number of produced details on this plant change?

Answer 1

Answer:

6.4%

Step-by-step explanation:

Given:

Productivity of new machine = 12% greater than last model

Number of new machines = -5%

Let's take number of machines = n

Take p as productivity of each machine.

Total productivity = np.

Productivity of new machine will be:

(100% + 12%) * p

= 112%.p

= 1.12p

Number of new machines will be:

(100% - 5%) * n

= 0.95n

From the calculations, total productivity will now be

1.12p * 0.95n

= 1.064np

Percentage Change in total productivity will be:

$= \frac{new productivity - old productivity}{old productivity} * 100$

$= \frac{1.064np - np}{np} * 100$

Converting np to 1 (or any number of your choice), we have:

$= \frac{(1064*1)-1}{1} * 100$

= 6.4%

Therefore, the percentage change = 6.4%

Answer 2

The total number of produced details increased by 6.4%

suppose the starting number was x. 
suppose x=100
100 +12%= 112
112-5%=106.4
106.4-100=6.4
6.4%