Question

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

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%

Answer 2

Answer: 6.4 %

Step-by-step explanation:

Let the productivity of old machine = x ( Initial production )

By the first machine the productivity of the machine is increased by 12 %.

Thus the productivity of the first machine = old productivity + 12 % of old productivity = 112 % of x = $\frac{112\times x}{100}$ = 1.12x

And, By the second machine the productivity of the machine is decreased by 5 %.

Thus the productivity of the second machine =first machine productivity - 5 % of first machine productivity = 95 % of 1.12x = $\frac{95\times 1.12x}{100}$ = 1.064x ( Final production )

Thus, the total change in the production = Final production - initial production = 1.064 x - x = 0.064 or 6.4 %

Therefore, the the number of produced details on this plant changes by 6.4 %.