A company produces on an average 4000 items per month for the first 3 months. How many items it must produce on an average per month over the next 9 months, to average 4375 items per month over the whole?

The company produces on average 4000 items per month for the first 3 months

$$\therefore$$ Total items produced in the first 3 months = 4000 $$\times$$ 3 = 12000

Let the company produce on average x items per month for the first 9 months

$$\therefore$$ Total items produced in the next 9 months = x $$\times$$ 9 = 9x

It needs to average 4375 items per month over the whole.

$$\therefore$$ Total items prouduced in 12 months = 4375 $$\times$$ 12 = 52500

$$\Rightarrow$$ 12000 + 9x = 52500

$$\Rightarrow$$ 9x = 40500

$$\Rightarrow$$ x = 4500

Hence, option C is the correct choice.