Could you help with the concept of ratio and income/expenditure? Incomes of  $A$  and  $B$ are in the ratio  $4:5$  and expenditures are also in the ratio $4:5$. Who saves more?
Options:
I) A
II) B
III) both save equally
IV) cannot be determined on the basis of the information provided
We've tried solving this by taking Income of A = 4x and expA = 4y, Inc B as 5x and exp B = 5y. But these are all ratios so there's  no way of actually determining the value. We tried hypothetically taking A:B actual values as 40:50, and savings as 4:5, and here were getting B saves more. But we have no way of knowing if that would always apply.
There are also different variations of the question where the expenditure is in different ratios, 5:6 as an example. The popular opinion of my group seems to be the answer would be CBD regardless. 
 A: You've started in the right direction, but you've kept your equations separate; the key part is figuring out how to combine the equations you've gotten to represent the information you've been given.
In this case, you have $$Inc(A)=4x,\quad Inc(B)=5x,\quad Exp(A)=4y, \quad Exp(B)=5y.$$
Alright, but the problem is asking about the savings $A$ and $B$ make - how does savings relate to income and expenditure?
Well, this is just: $$Sav=Inc-Exp.$$ So we have $$Sav(A)=Inc(A)-Exp(A)=4x-4y,\quad Sav(B)=Inc(B)=Exp(B)=5x-5y.$$
That's step one. Now, we want to compare these two quantities. That is, we're asking:

Which is larger, $4x-4y$ or $5x-5y$?

So let's subtract the first from the second; if the difference is positive, the second is bigger, and if it's negative the first is bigger, and if it's zero they're equal.
This difference is $$(5x-5y)-(4x-4y)=x-y.$$
So now the entire problem boils down to:

Is $x-y$ positive or negative?

Do you think this is a question that you have enough information to answer, or does it depend on what exactly $x$ and $y$ are? What does this tell you about the answer to the whole problem?
