An art dealer bought a painting for $70 and sold it for $80. Later, he bought it back for $90 and sold it again for $100. In the end, did the dealer make a profit, incur a loss, or break even? How much did he make or lose?
This math question has gone viral, stumping internet users time and again over the past few years.
Every time it’s posted, it attracts a flood of comments with users debating the answer among themselves.
Opinions vary widely, with some suggesting the art dealer made a $10 profit, others $20, and still others $30. So, what’s the correct answer?
The main source of confusion seems to be that the dealer sells the painting for $80, then buys it back for $90, which can make it look like he spent an extra $10.
However, the key to solving this puzzle is to view each transaction as a separate step.
Once you do, there are several straightforward methods to find the solution.
Here are the simplest approaches you can use.
Method 1: Transaction-by-Transaction Profit Calculation
In this approach, we’ll look at each transaction one by one to see if the dealer made a profit or a loss, then add them up at the end.
First Transaction:
The dealer bought the painting for $70.
He then sold it for $80.
Since he sold it for $10 more than he paid, he made a $10 profit on this transaction.
Second Transaction:
The dealer bought the painting back for $90.
He sold it again for $100.
This time, he also sold it for $10 more than he paid, so he made another $10 profit.
Final Result:
Add up the profit from each transaction: $10 + $10 = $20 profit.
So, by adding the profits from each transaction, we find that the dealer made a total of $20 profit.
Method 2: Net Cash Flow Analysis
In this approach, we’ll look at how much money went in and out of the dealer’s pocket over all the transactions.
Starting Point:
Let’s start by keeping track of how much the dealer spends and earns.
First Transaction:
The dealer spends $70 to buy the painting (so he’s down by $70).
He sells it for $80, so now he has $80 in his pocket.
Second Transaction:
The dealer spends $90 to buy the painting back (so he’s down by $90).
He sells it again for $100, so now he has $100 in his pocket.
Final Result:
If we add up all the money he spent ($70 + $90 = $160) and all the money he earned ($80 + $100 = $180), we can find the total profit by subtracting the spending from the earnings: $180 – $160 = $20 profit.
So, using the Net Cash Flow Analysis, we also find that the dealer made a $20 profit in the end.
Method 3: Algebraic Equation Approach
In this approach, we’ll represent the transactions with variables to find the dealer’s total profit or loss.
Let:
- B1 be the amount he bought the painting for the first time ($70).
- S1 be the amount he sold it for the first time ($80).
- B2 be the amount he bought it for the second time ($90).
- S2 be the amount he sold it for the second time ($100).
Now, we can set up an equation to calculate the total profit or loss by subtracting the total amount he spent from the total amount he earned.
Step 1: Write the Profit Equation
The dealer’s total profit or loss can be calculated with this formula:
Profit = (S1+S2)−(B1+B2)
Step 2: Substitute the Values
Now, we plug in the values:
Profit= (80+100)−(70+90)
=180-160
=20
Final Answer
So, the dealer made a $20 profit.
Similar Math Problems/Puzzles
Problem # 1
I bought a goat for $20,000 and sold it for $30,000. Then, I bought it back for $40,000 and sold it again for $50,000. What was my total profit?
Similar to the previous problem, there are several approaches you can use to solve this. To keep it simple, let’s go with the first approach: Transaction-by-Transaction Profit.
Let’s break down each transaction to calculate the total profit.
First Transaction:
You bought the goat for $20,000.
You sold it for $30,000.
Profit for this transaction: $30,000 – $20,000 = $10,000.
Second Transaction:
You bought the goat back for $40,000.
You sold it again for $50,000.
Profit for this transaction: $50,000 – $40,000 = $10,000.
Total Profit:
Add up the profits from both transactions: $10,000 + $10,000 = $20,000.
So, your total profit is $20,000.
Problem # 2
A man buys a horse for $60. He sells the horse for $70. He then buys the horse back for $80. And he sells the horse again for $90. In the end, how much money did the man make or lose? Or did he break even?
Let’s break down each transaction to calculate the total profit or loss:
First Transaction:
The man buys the horse for $60.
He sells the horse for $70.
Profit from this transaction: $70 – $60 = $10 profit.
Second Transaction:
He buys the horse back for $80.
He sells it again for $90.
Profit from this transaction: $90 – $80 = $10 profit.
Total Profit:
Add up the profits from both transactions: $10 + $10 = $20 profit.
So, the man made a total of $20 profit in the end.
Problem # 3
I bought a cow for $800. I sold it for $1000. I bought it again for $1100. I sold it again for $1300. How much did I earn?
Let’s break down the transactions:
First Transaction:
You bought the cow for $800.
You sold it for $1000.
Profit from this transaction: $1000 – $800 = $200 profit.
Second Transaction:
You bought the cow again for $1100.
You sold it for $1300.
Profit from this transaction: $1300 – $1100 = $200 profit.
Total Profit:
Add up the profits from both transactions: $200 + $200 = $400 profit.
So, you earned a total of $400.