Ratio

This is a neat question! It's a really easy problem you've seen before in disguise.

Because we know these are linearly related, we are basically being told that

S = Rx +b where x is some multiple and b is a constant.

does this look familiar yet? We're basically being given two points on the x/y coordinate plane, being asked to find the equation of the line and a 3rd point on the line.

Let's plug in some values from the conversion we know.

30 = 6x +b
60 = 24x +b

Combine these to get:
30 = 18x
x = 30/18 = 5/3

Then we can solve for b:
30 = 6* (5/3) +b
30 = 10 +b
b = 20

Or by combining the two equations:
120 = 24x + 4b
60 = 24x +b
60 = 3b
b = 20

So the conversion between R and S is as follows:

S = (5/3)R +20

Since we're looking for S=100, let's just throw it in!

100 = (5/3)R + 20
80 = (5/3)R
240/5 = R
R = 48

So the answer is 48!

When you rewrite the numbers of the question you see ratios are different,
so you need to find another way to link the two relations (30;6) and (60;24).
This word can help you: "A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly."
So you resolve it with y=ax+b