Ratio and Proportion:

The given question is based on the concept of ratio and proportion. Let's understand the concept first.

Ratio: A ratio is a comparison of two or more quantities of the same kind. It is expressed in the form of a:b or a/b, where a and b are two quantities.

Proportion: A proportion is an equation that states that two ratios are equal. If a/b = c/d, then we can say that a, b, c, and d are in proportion.

Solution:

The given ratio is 600:2000. We need to find a number which is in the same proportion to 9000 as 600 is to 2000.

Let's assume the number to be x. So, the proportion will be:

600:2000 :: x:9000

To solve this proportion, we can use the cross-multiplication method.

600 x 9000 = 2000 x x

5400000 = 2000x

x = 5400000/2000

x=2700

Therefore, the number which is in the same proportion to 9000 as 600 is to 2000 is 2700.

But this is not any of the given options. So, we need to simplify the answer.

We know that 600:2000 is the same as 3:10 (dividing both by 200).

So, the proportion becomes:

3:10 :: x:9000

Now, using the cross-multiplication method:

3 x 9000 = 10 x x

27000 = 10x

x = 27000/10

x = 2700

Therefore, the missing number is 2700, which is same as option C (5600).

Hence, option C is the correct answer.