1955 AHSME Problems/Problem 26

Revision as of 12:01, 18 November 2020 by Angrybird029 (talk | contribs) (Created page with "Mr. <math>A</math> owns a house worth <math>\textdollar{10000}</math>. He sells it to Mr. <math>B</math> at <math>10</math>% profit. Mr. <math>B</math> sells the house back to...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Mr. $A$ owns a house worth $\textdollar{10000}$. He sells it to Mr. $B$ at $10$% profit. Mr. $B$ sells the house back to Mr. $A$ at a $10$% loss. Then:

$\textbf{(A)}\ \text{Mr. A comes out even}\qquad\textbf{(B)}\ \text{Mr. A makes } \textdollar{ 100}\qquad\textbf{(C)}\ \text{Mr. A makes } \textdollar{ 1000}\\ \textbf{(D)}\ \text{Mr. B loses } \textdollar{ 100}\qquad\textbf{(E)}\ \text{none of the above is correct}$

Solution

Assume that Mr. $A$ has $\textdollar{10000}$ to start with (the house) and Mr. $B$ has $\textdollar{11000}$

$A$ sells the house to $B$ for $\textdollar{11000}$, leaving Mr. $A$ with $\textdollar{11000}$ and Mr. $B$ with $\textdollar{10000}$.

Then, Mr. $B$ sells the house back to Mr. $A$ for $\textdollar{9000}$, which leaves $A$ with $\textdollar{12000}$ and $B$ with $\textdollar{9000}$.

We can see that $A$ gained $\textdollar{2000}$ out of Mr. $B$'s expense, but none of the options says this. We can therefore conclude that the correct answer is $\boxed{\textbf{(C)}}$.

See Also

1955 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 25
Followed by
Problem 27
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
All AHSME Problems and Solutions


The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png