Problem:
Mr. A owns a home worth $10,000. He sells it to Mr. B at a 10% profit. Mr. B sells the house back to Mr. A at a 10% loss. Then:
Answer Choices:
A. A comes out even
B. A makes $1,100 on the deal
C. A makes $1,000 on the deal
D. A loses $900 on the deal
E. A loses $1,000 on the deal
Solution:
Let S1 be the price Mr. A sells the house for, and S2 be the price he buys it back for. The house is initially worth $10,000.
First, Mr. A sells the house to Mr. B at a 10% profit. The selling price is:
S1=$10,000×(1+0.10)=$10,000×1.10=$11,000
Next, Mr. B sells the house back to Mr. A at a 10% loss. Mr. B's loss is calculated based on his purchase price of $11,000. The new selling price is:
S2=$11,000×(1−0.10)=$11,000×0.90=$9,900
Mr. A's overall profit is the total cash he received minus the total cash he paid out, since he ends up with the house he started with.
A’s Profit=(Cash In)−(Cash Out)=S1−S2=$11,000−$9,900=$1,100
Therefore, Mr. A makes a profit of $1,100 on the deal.