My brothers share from income. My brother is driving a limo with his partner who told him that they will go $50-50$ on income and also $50-50$ on gas. 
So if my brother earns $\$1000$ by spending $\$200$ on gas, what will be my brothers share and what will be his partners share?
So you have to calculate what my brother should get from the $\$1000$ and what his partner should get taking into consideration the spending on gas (is spent by my brother).
 A: OK, so your brother and partner spend 200 on total and get 1000 back. This means your brother should pay 100 of the 200 and get 500 of the 1000 back. This way he gets 400 profit. Since However: taking into account that your brother paid the full 200 he should get 600 of the 1000 and give 400 to the partner. This way both of them make a profit of 400.

Tutorial

There are two possible scenarios: I don’t understand which one applies to you.

Scenario 1.

Your brother paid for the full amount of gas: In this scenario the partner needs to give him 600 bucks to compensate for the 200 he spent on the gas. This way they both get 400 profit.

Scenario 2.

Your brother and his partner both paid 100 dollars to buy the gas. In this case they should both take 500 out of the 1000 to get 400 profit.
A: Okay, I'm the brother LOL.
Let me do the economics of the total
Revenue = \$1000 = \$800 + \$200
Profit = \$800
Spending = \$200
Now 50% profit and 50% spending
Profit = \$400
I should be paying only \$100 for the gas But I spent the full share of the gas
So now I should ask my partner to pay that extra \$100 I spent on gas
Let's look at the share now
My share: profit = \$400 and spending = \$100
His share: profit = \$400 and spending = \$100
Now the revenue for both is \$500 with equal share of profit and spending.
I think its pretty clear from my ecnomics calculations.

Edit: I forgot to mention. We are also splitting the expenses. I think that was the missing piece.
A: Both you and your brother calculations are correct. You remove the expenses and split the profit: 
Revenue - Expenses = Profit 
share = Profit/2 

1000 - 200 = 800 
800 / 2 = 400
Both should get $400 of **profit**.

He splits the revenue and the expenses:
(Revenu/2) - (expenses/2) = share
(1000/2) - (200/2) = 500 - 100 = 400
Both should get $400 of **profit**.

As far as the computation goes, the result is the same. They both get \$500 of the revenue except for the fact that the revenue money doesn't exist if your brother collected the money and paid the expenses. Once you have paid the expenses, what is left is profit, not revenue.
The problem here is that we don't know who got the $1000. We know your brother paid \$200, but we don't know who collected the \$1000. 
If your bother collected the money and paid the expenses, what is left is profit: he owes \$400 to his partner. If he likes, he can give \$500 to his partner and take \$100 back. No difference.
If his partner collected the money but did not pay the expenses, what he has is revenue, he owes your brother \$600. His partner can also give him \$500 for his share of the revenue, and \$100 for his share of the expenses.
Worth mentioning that whoever owns the car is the sucker in this deal, because the real cost of the car is quite a bit in excess of the gas in the tank. There are insurance fees, maintenance, repairs, depreciation, risk, etc. which all add up to the actual cost of driving the car. Roughly, if you spend \$200 on gas, there is about \$100 in hidden costs. 
