Can anyone please explain this math problem?

Hi,
There is a decrease in the number of students, say s%...
Then the student who were initially 5500 goes down to 5500*(100-s)/100..
Example.. the decrease was 20%, so number is 5500*(100-20)/100=5500*80/100..
Similarly for increase in faculty (100+F)/100..

Thank you so much chetan2u for your explanation Kudos to you ..
But the answer given is
(100+S)/(100+F) * R

Since Students decrease, it should be 100-s right ?

I think the process used is completely right, but there is a minor flaw.
S represents the change and not the decrease itself. The change has to be used as +S, and when the change is on the negative side (there is a decrease), S will assume a -ve value.

Example: If there is an increase, S = +5%, or in case of decrease, S = -7%
Over here in the working provided, in case of increase, S = -5% and in case of decrease, S = 7%. The general way of depiction is wrong.

Working is totally fine though.

Hope it helps

Thanks testprepabc

But they have provided S is decreasing right ?
Since the value is not given .. we are giving a general expression ?

The question defines S to be a percentage change in the number of students. We need a formula which will generalize both the increase and the decrease. Hence the positive sign.
Small example: Let's say the question had 2 parts - One with a x% increase and the other with a x% decrease.
The easiest way to answer this is to write a formula which will satisfy both the equation instead of writing 2 formulae one with +S and the other with -S. Rather you would probably write a formula with +S and replace +S = x% for increase and +S = -x% for decrease.
A mathematical corollary would be formula for compound interest. We do not change the +ve sign in the bracket to -ve for decreasing Rs in A=P[1+(R/100)]^n, rather replace R with a -ve value.

Remember, formulae should be general and conventional.

Hope this explains and helps you