Basic arithmetic problem, please help out.

You assign the variable x to one person, say person A spends x. The other one is fixed then. Then B must spend 1000 - x. When you make your desired equation, you will get the value of x. Now you know that person A spends x and B spends 1000 - x. If A spends more, automatically x will be greater than 1000 - x.
You can also go the other way around - B spends x while A spends 1000 - x. Your equation will change now and values of x will change too. Now x will be less than 1000 - x. B spends x and A spends 1000 - x.
The final answer will be the same in both the cases.

or if you talk about the question in OG, you can assign x to stocks that went down and make the equation as
(120/100)x + x = 2420
x = 1100 = stocks that went down
2420 - x = 1320 = stocks that went up

or
you can assign x to stocks that went up and make the equation as
x + (100/120)x = 2420 (x is 20% more than the stocks that went down so x = (120/100)*stocks that went down )
x = 1320 = stocks that went up
2420 - x = 1100 = stocks that went down

Notice that values of x in the two cases are different (since x stands for different things) but overall the answer is the same.