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Fractional Distillation and Reflux Ratios

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What is the significance of reflux ratio in fractional distillation? Also what exactly does the formula, Ya/Yb = Pa/Pb = PaNa/PbNb, mean in terms of fractional distillation?

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The following definition for reflux ratio is from http://www.solvent--recycling.com/reflux%20ratio.html
"The Reflux ratio is the ratio between the boil up rate and the take-off rate. Or in other words, it is the ratio between the amount of reflux that goes back down the distillation column and the ...

Solution Summary

A definition of reflux ratio is shown, as well as the significance of certain equations associated with fractional distillation.

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Problem:
A saturated liquid mixture containing 60 mole % benzene and 40 mole % toluene is to be distilled continuously into a distillate product containing 90 mole % benzene and the bottom product containing 5 mole % benzene. The fractional distillation column will operate at approximately constant pressure of 1 atm. The reflux ratio is 2. How many theoretical plates must the column have if the feed is introduced into the eighth plate? Equilibrium data are:
x 0 0.017 0.075 0.13 0.211 0.288 0.37 0.411 0.581 0.78 1
y 0 0.039 0.161 0.261 0.393 0.496 0.591 0.632 0.777 0.9 1

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