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 change would be 6.4%

Step-by-step explanation:

Let x be the number of productivity of each machine and y be the numbers of machines,

That is, the total original productivity = number of machines × productivity of each machine

= xy,

If productivity of each machine is increased by 12%,

New productivity of each machine= (100+12)% of x

= 112% of x

= 1.12x

Now, if also the number of machines are decreased by 5%,

New models = (100-5)% of y

= 95% of y

= 0.95y

Thus, total new productivity = 1.12x × 0.95y = 1.064xy

Hence, the total change in productivity = $=\frac{\text{New - Original}}{\text{Original}}\times 100$

$=\frac{1.064xy-xy}{xy}\times 100$

$=\frac{0.064}{1}\times 100$

= 6.4%

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