Percentage increase/decrease- WHAT should be the denominator??

OK, so at many times we get confused between what should be the base or denominator when we are looking for a % increase or a % decrease. I had few students asking this through PMs and seen few on the forum with the same query.

You choose the wrong one and you will still find your answer in the choices as the test makers are looking for you to commit these mistakes

So, choosing the correct denominator is very important. It may be a very easy thing for a person who is thorough with % problems and on other hand it may be a very taxing job for someone else.

When we are looking at such question, a simple rule would be to see what comes after THAN and almost everytime you should be correct.

(I) R is what % less than T.
So, we have T after THAN, thus T becomes the denominator or the BEFORE value and R becomes the AFTER value..
% decrease = \(\frac{before-after}{before}*100=\frac{T-R}{T}*100\) .

(II) Say, now the question read - T is what % more than R
So, we have R after THAN, thus R becomes the denominator or the BEFORE value and T becomes the AFTER value..
% increase = \(\frac{after-before}{before}*100=\frac{T-R}{R}*100\) .

A question on the same concept

The number of television sets sold by Store R last month was approximately what percent less than the number of television sets sold by Store T last month? ( The number of television sets sold by Store R was 20 and number of television sets sold by Store T was 45 as per the attached figure)

A) 40%

B) 56%

C) 86%

D) 95%

E) 125%

so simplify it -
R is what % less than T
so T is after THAN and becomes BEFORE and R becomes AFTER.

Now we are looking for % less = \(\frac{Before-After}{Before}*100=\frac{45-20}{45}*100=\frac{2500}{45}=55.55\)% or ~56%

But say you took the other way \(=\frac{45-20}{20}*100=\frac{2500}{20}=125\)% .. AND the wrong answer is there in the choice.
so be careful

I would add more examples with a slight different wordings slightly later