I was so shocked when I saw this posted elsewhere and how many people couldn’t get it right and insisted that they did, I thought I’d try this here. There IS only one answer.

The interesting part about this is how many people saw those 4 simple statements in a word problem and just added backstory to the point it got them to the wrong answer. Everyone saying $300 just ASSUMING there needed to be money borrowed or loaned in order to buy the second cow for NO reason. No need to overthink it. It doesn’t matter that it’s the same cow. Nothing implies that the sale of the first cow was even necessary to buy the second cow. Those are distractions. Don’t fall for it.

The problem is that people are assuming that the initial $800 is the total cash the initial purchaser has on hand. That gives a total of $300 in profit at the end with a loan of $100 being required for the second purchase.
But, that assumption is incorrect based on the wording.
The original purchaser merely states how much they bought the cow for. Not how much cash they had on hand. That means we can assume, in purchasing the cow the second time, there was $100 available for the price increase

To people who thought they "lost" 100 in between: With that way of thinking you also lost 800 in the beginning first time you bought the cow for 800.

Imagine you had 5k. You spent 800 to buy, you now have 4200. You sold it for 1k, you now have 5200. You bought it again for 1100, you now have 4100. You sold it again for 1300, you now have 5400.

What you start with doesn't matter. Imagine 0, you borrowed to buy the cow both times. You return the money and pocket the difference, which is 400.

I've been doing accounting for 10 years now, and if you only take into account buying and selling, not maintenance, transport, care, selling Milk (meaning it could also be a TV or a refrigerator) then there can't be a single answer. The only financially sane way to look at this is how much of the initial profit you need to buy the cow a second time. And you subtract that from your 400 max.
If you already have 1100 $ at the start, then your profit is 400$.
You had only 900$ ? Only 200$.

I have $800 in my wallet. I buy a cow with it. I have $0 in my wallet now.
I sell the cow for $1,000. I have $1,000 in my wallet now.
I want to buy an $1,100 cow, but I only have $1,000, so I borrow $100 from a friend and use his $100 + my $1,000 to buy the cow for $1,100. I have $0 in my wallet now, plus I owe my friend $100.
I sell the cow for $1,300. I pay my friend his $100 back. I have $1,200 in my wallet now.

Since I started with $800 and am ending with $1,200, I am $400 richer.

The issue people are tripping up here is that they’re not considering that the guy has ANY OTHER MONEY than what he has within the problem.

Once you open it up you see it’s clearly two transactions:

800 -> 1000 = 200$
1100 - > 1300 = 200$

It says “profit” so each time the guy made 200$ profit. The second sale does NOT negate the first one.

If it’s just the money in the problem then it’s still 400$: 800 -> 1000 = +200; 200 - 1100 -> -900; - 900 -> 1300 = +400$

I asked Claude AI:
Total profit: $400

The key is to treat each buy/sell pair as an independent transaction:
Transaction 1
∙ Buy: −$800
∙ Sell: +$1,000
∙ Profit: +$200
Transaction 2
∙ Buy: −$1,100
∙ Sell: +$1,300
∙ Profit: +$200
Net: $200 + $200 = $400

The cleaner way is to simply track total cash in vs. total cash out:
∙ Cash out: $800 + $1,100 = $1,900
∙ Cash in: $1,000 + $1,300 = $2,300
∙ Net profit: $2,300 − $1,900 = $400

In terms of economics you represent outgoing money with a negative sign and incoming money with a positive, and then you proceed to column all movements, like this:
-800 (first buy)
+1000 (first sell)
-11000 (second buy)
+1300 (second sell)
------------
400 (profit)
Then you have a lot of other terms and calculations, according to your financial status before all this movements, but keep in mind you have to stay focused on the question, which is profit = 400.

For those who still don’t understand why the profit is 400. Let me explain the other way.

You have 900 in your pocket. You buy a cow of 800. Now you have 100 in your pocket.
Sell it for 1000. Now you have 1100 in your pocket.

Buy a cow again for 1100. Nothing left in your pocket.

Finally you sell a cow for 1300.
So finally you have 1300 in your pocket.

You start with having 900 now you have 1300
Profit is 1300-900=400.
Got it?

No, when you buy the cow for 800 and have 100 left, the 100 isn't profit. It's your personal money. You don't count this.

it wasn't counted. the answer is $400.

The key word is profit. Ignore the word "again". The order doesn't matter. You could buy the $1100 cow first, or make it a new cow and buy it at the same time. It makes no difference to the equation or answer. You make $200 profit twice, so $400 total profit. Where the extra money for the $1100 cow comes from is irrelevant, just like where the $800 for the first cow comes from is irrelevant (since no loan costs are mentioned).

I used this scenario with my math students. I asked their thoughts on the answer, and got a variety of responses. I then had the kids divide themselves into camps according the possible solutions. They then would try to convince others to join their camp. It was a great exercise in persuasive arguments. Eventually, we enacted the scene using play money (including a student who played the cow) to illustrate the result.

Well you'd start with your gross profit of $400, but if you housed and fed/watered the cow for periods of time and paid their vet bills etc, you'd naturally have to take those costs plus any purchase and sale costs off to get to the net profit. If you sold the milk from the cow then that's added income, less milking and other costs. Hard to say what the actual profit it before knowing the rest of the info 🐄

It's cow futures, not real cows. No serious business deals in the real world any more

People need to practice practical problem-solving methods. If you have a problem like this, you can easily check it by plugging in a number and going step by step. Assume you start with $1000. 1) Buy the cow for $800. $200 on hand. 2) Sell the cow for $1000. $1200 on hand. 3) Buy the cow for $1100. $100 on hand. 4) Sell the cow for $1300. $1400 on hand.

Original cash on hand was $1000, so profit is $400.

If your base capital is 800 then on 1st sale you profited 200. Since it's your profit I'll assume you got to keep on your personal needs thus means we are only considering the base capital which is 800. On 2nd transaction you got to loan 300 to afford the 1100 then sold that for 1300. This gross minus base capital(800) minus repayment(300) means you profited again another 200. So 400 in total?

You get 400 even if you treat this as a logical language problem: there are four transactions (2 to buy, 2 to sell) and you invest a total of 900 (800 in the 1st transaction + an additional 100 in the third one), and at the end of the 4th transaction you have a total of 1300. So 1300 - 900 = 400.
(The risk of treating it as a language problem is overlooking the second investment of 100.)

That's clearly a dairy cow. No matter who is doing the math, they aren't taking into consideration the profits from breeding and milking the cow that aren't mentioned here. Or the costs of feeding and caring for it. You have to tell me how big the farm is, how much the bank is involved, and if there are any government subsidies before anyone can tell you if the $400 is profit or not.

there is no singular, universal "profit"

American business practice commonly has gross and operating profits under GAAP and other accounting methods

almost everything, if not everything, in the universe is relational and/or is coherently defined over some period as well, usually time

the answer here is to reject the question or ask follow ups, not to insist on any answer

Actually there is no way to answer this because there is not enough information. Did you feed the cow? How much did the feed cost? What about vet bills? I am sure you had the cow looked at by a vet at least once.
Even assuming that the cow was just stuck in a pasture and left to fend for itself how did you get it to and from the point of sale?

The mistake some make is to assume the starting $800 is all the money available. But that can’t be true because $100 of the repurchase price of our bovine friend came from somewhere other than the first cow sale. Hence, there were two separate transactions, each with a $200 profit. So $400 profit. Amount in the bank $1300 to infinity.

Thank you for pointing out the 100

Total sales income $2300 less total cost prices $1900 = $400 gross profit. I would advise deducting any other allowable expenses such as advertising, rented vehicle transportation, fuel if bought for that journey only, refreshments and sundry expenses, all must have a receipt, to get to a low nett profit for the tax records. 😉😝

Profit is unknown. You have revenue of $2,300 and $1,900 in product cost. But since you don't having any expenses like feed, vet bills, labor and transportation listed and capital expenses like land and fencing. There is no way to know what your profit is. Mistaking revenue for profit is the main reason most businesses fail.

The only way to look at this is …
What did I start with ? (800)
What did I add along the way ? (100)
What did it finish with ? (1300)

When the question says I re-bought the cow people’s brains go crazy … at that point you added 100 to rebuy so 1300 now minus the 100 added minus the original starting 800 = 400 profit

$400. The argument same cow matters is irrelevant. There’s nothing stating he doesn’t have money to cover the jump to $1100. He sold the cow each time for $200 dollars meaning he made $400 dollars. It only matters at what price he buys and sells. Not the difference between his sale price and new buy price.

You make 400 dollars. People make the mistake of thinking of the cow as the issue ie it could easily be two different cows . So if oyu had 2 grand you buy something and sell it for two hundred extra you then have 2200 you then by something else and sell it for 200 extra you now have 2400 . End of story

I'm amazed at how many people can derive any answer other than $400.

These are two separate transactions, each of which results in a profit of $200. It doesn't matter whether it is the same cow, two different cows, or two completely different items for sale.

$200 + $200 = $400 TOTAL PROFIT.

$300. Buy the cow for $800 and sell it for $1000, $200 profit. When you buy for $1100 your have a $100 loss so you are down $100 from the previous sale but when you sell it again for $1300 you have an additional $200 profit. In the end you only have a $300 profit. Now go buy a cow for $300.

You bought the cow for 800 and sold that cow for 1000. So at that point you are up 200.
Then you buy a cow for 1100, so at that point you are down 900. Then you sell it for 1300, so you’re now up 400.
It’s two separate transactions where the profit on each transaction was 200.
It’s very simple maths, primary school level.

For everyone trying to be clever by saying you don’t know the profit because you don’t the know the other expenses, I say, really? No-one likes a wise-ass. If it helps, think of the 400 as gross profit and everything else as part of the expenses that will determine the nett profit/loss.

800 is what I have in assets. No other assets mentioned in problem.
Cow = 800
Cow sale= 1000
200 profit
Cow purchase = 1100 ( 100 must come from loan or debt arrangement)
Cow sale = 1300
200 profit- 100 taken from profit for debt arrangement =100 dollars profit
300 dollars total profit

Paid 800 sold it 1000 .
Bought it back for 1100. You only have 1000. Had to borrow 100.
Thank God you sold it for $ 1300.
After you pay back the 100 you borrowed .
You got $100. What a sorted Journey . Should have slaughtered the cow the first time. Would've made a bundle.

After you pay back the 100 (that someone gave you) you still have a 400 profit. Even if you borrowed 100 or 1100 to buy the cow the second time, and paid it back, you still have 400 profit.
It’s primarily school level maths

I did the match and it equals $300. But when I'm a guy , and I sell a cow, it comes out just like I said. That guy doesn't have $400 in his pocket when he sells it for 1300. I just showed you

You are ignoring the +100 that someone gave you.
1. Buy 800 sell 1000= 200 profit.
2. Borrow 100= +100 in your pocket.
3. Buy 1100 (1000 of your money and 100 you borrowed) sell 1300= 200 profit
4. Pay 100 back.
Summary:
+200 from 1,
+100 from 2,
+200 from 3,
-100 from 4,
Total profit =400
It’s the same result if they borrowed 1100, or they had 10,000 in their pocket. It’s always 400 profit.

OK I bought a cow for $ 800. Sold it for $1000. So I have $1000. .
Not $1100. So now I need $ 100 because for some reason, I decide this cow I had. Cant live without him.
So I buy him back. That's all the money I got. There's not $200 laying around. I owe a guy $100.
So now I say...Ok
OK. I'll sell this stinky cow for $1300 , pay back that $100, and at least I aint broke.

You had total outgoings of 1,900 and total incomings of 2,300 so profit is 400

Not sure how people are arriving at anything different unless they’re saying well what about upkeep, contribution to the costs of the barn and how much did it eat and drink whilst you owned it

This isn't a math problem, it's a language problem. It makes people mess up the math by deliberately presenting the problem in a way that confuses people based on how they compartmentalize information. This is obviously intentional or else they wouldn't frame it this way.

Just start with a balance of 0. Pretend you are buying on credit.
Starting balance: 0
Buy cow $800: -800 balance
Sell cow $1,000: +200 credit
Buy cow$1,100: -900 balance
Sell cow$1,300: +400 credit
Start with a zero and end with a $400 credit.

$400 profit, final answer.

Pretend you start with $1000 and no cow

first transaction: -$800, +1 cow
total: $200, 1 cow

2nd transaction: +$1000, -1 cow
total: $1200, no cow

3rd: -$1100, +1 cow
total: $100, 1 cow

4th: +$1300, -1 cow
total: $1400, no cow

$1400-the original $1000=
profit: $400

Easy…subtract all the money you spend besides the profit from 1300

800 = capital
1. 1300 - 800 = 500

You spend another 1100 meaning since your total money from the transaction is 1000 meaning you spend another 100 from your capital

2. 500 - 100 = 400

400 profit

So I’m going to assume I have 900 as capital
Bought a cow for 800 - I have 100 cash
Sold the cow for 1000 - I currently have 1100 cash
Bought the cow with that 1100 - the sold it for 1300

Being 900 is my capital and my current money is 1300, yeah my profit is 400

$100? Say you start with $800. Sell for $1000. Now you made $200 and now have $1000. If you buy it for $1100, how, if you only have $1000. So you're $100 in the negative. Sell for $1300. You take $100 to reach $0. $1200 goes to you. That's $100 profit.

Start with 1100

Buy cow. You have 300 and a cow.

Sell cow for 1000. Now you have 1300.

Buy cow for 1100. You have a cow and $200

Sell cow for 1300. You have 1500

Overall you have made $400. This works with any amount of money to start with.

You didn't make $400 profit, you lost money. Does anyone know what it costs to maintain a cow? There's feed, housing costs, daily upkeep and clean up, vet bills, business insurance. Don't forget to deduct business expenses from your taxes.

Let me make it easy.. in business you have cost of goods and sales. Cost of goods: $800+1100 same cow different cow doesn't matter = $1900 (the amount of money out of for product) Sales: $1000+$1300 = $2300 - $1900 (cost of goods) = $400