Hello Fa Aa,

There are two main possibilities, the first of which is that the Qubit working solution was not at the right concentration in the sample.  This can be confirmed by running a standard of any other DNA/RNA that you have handy.  The Qubit system is more sensitive than a spectrophotometric assay, which is able to quantify 250 pg/ul to 1 ug/ul in comparison to UV, which can detect on the order of 2 ng/ul to 15 ng/ul.  However, it is also more specific due to the fluorescent endpoint, meaning that if your UV measured sample is contaminated by free nucleotides, salts, or other organic compounds that can be found in solvents which also have an absorbance around 260 nm.  This is the second possibility: contamination, especially if the concentration on the UV is also low

Did you do a gDNA elimination step?

The Nanodrop is measuring any nucleic acid, so you might have DNA present, or possibly just degraded nucleotides. The Qubit is measuring whichever reagent you use. So both might be giving you the correct answer, you have little or no undegraded RNA but plenty of DNA or nucleotides. 

I completely concur and cannot really add to basic explanations described in answers

I will however add one more thing: if not already done it might be an idea to DNAse treat and then ethanol precipitate the RNA or simply ethanol precipitate the RNA.  In particular if you precipitate the RNA using 3 volumes of ethanol plus 2M ammonium acetate in place of 0.3M sodium acetate you will selectively precipitate just RNA species above 100bp and so will and is traditionally used to remove nucleotides. By eliminating nucleotides nano drop at 260 will more accurately reflect total RNA levels and thus mirror quit readings which just detect whole undegraded RNA 

What is more a 70% ethanol wash of ppt nucleic acid you will more fully eliminate salt contributing to 260 nano drop but not affect quit measurements. This washed precipitated material will thus more fully  mirror with bit readings 

Thanks for the thorough response! I I am trying to re-extract RNA and recheck the concentration