Can anyone please explain this math problem?

Question

Attached. Much obliged!

chetan2u · Answer

Hi,
lets see what all we have..
1) year 1999..
number of students=5500
number of faculty=5500/R..

2) year 2004.....
number of students=5500(100-S)/100..where S is the % change over 5 academic years
number of faculty=5500/R*(100+F)/100..where F is the % change over 5 academic years..
so number of students/number of faculty members= 
 / 
=(100-S)/(100+F) * R
ans D

Shrivathsan · Answer

Hi chetan2u , Can you please tell me how you got the below step ? 100-S and 100+F .. i din understand from where 100 came all of a sudden.. is there anything i am missing ? :oops:

just a query, is the answer (100-S)/(100+F) * R ? cause the one mentioned in screenshot is different.

chetan2u · Answer

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..

Shrivathsan · Answer

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 ?

testprepabc · Answer

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

Shrivathsan · Answer

Thanks  testprepabc

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

testprepabc · Answer

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 ^n, rather replace R with a -ve value. Remember, formulae should be general and conventional. Hope this explains and helps you

Can anyone please explain this math problem?

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