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A vendor bought two pre-owned cars for $\$ 5000$ and sold them for a p
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04 Apr 2025, 08:54
04 Apr 2025, 08:54
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A vendor bought two pre-owned cars for $\(\$ 5000\)$ and sold them for a profit of $\(\$ 1820\)$. He made a profit of $\(28 \%\)$ on one car and $\(42 \%\)$ on the other car. What is the cost price of the car on which he made a profit of $\(28 \%\)$ ?
(A) $ 1000$
(B) $ 2000$
(C) $ 3000$
(D) $ 4000$
(E) $ 5000$
(A) $ 1000$
(B) $ 2000$
(C) $ 3000$
(D) $ 4000$
(E) $ 5000$
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Re: A vendor bought two pre-owned cars for $\$ 5000$ and sold them for a p
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06 Apr 2025, 21:06
06 Apr 2025, 21:06
can someone please provide solution of this problem?
A vendor bought two pre-owned cars for $\$ 5000$ and sold them for a p
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07 Apr 2025, 00:48
07 Apr 2025, 00:48
Expert Reply
Hi
Usually the official solution to the questions is given after 4 or 5 days to give the time to the students to practice. However, this question can be solved also by a bit of math
28% or 0.28 of a = 1820/5000 because when someone makes a profit the formula is
\(\begin{aligned}
& \text { Profit } \%=\frac{\text { Profit }}{\text { Cost price }} \times 100 \\
& \text { Loss } \%=\frac{\text { Loss }}{\text { Cost price }} \times 100
\end{aligned}\)
Now
0.28 a= 1820/5000
0.28a=36.4*100
Essentially, 3640 is our overall profit but we need to depurate it from the 1820 which is also the 28% +42% profits. Therefore, it is inflated.
3640-1820=2020 which is B
Alternative approach
By inspection , we do not know car 1 initial cost or car 2. we only know that 5000 is the over all cost of both.
Now, if we have a 28% profit on the first one, it is reasonable to conceive that car 1 is the cheaper. Even if you assume that car 1 cost is 2000, the profit of 28% on 2000 is 2560.
therefore, an educated guess is surely B
Usually the official solution to the questions is given after 4 or 5 days to give the time to the students to practice. However, this question can be solved also by a bit of math
28% or 0.28 of a = 1820/5000 because when someone makes a profit the formula is
\(\begin{aligned}
& \text { Profit } \%=\frac{\text { Profit }}{\text { Cost price }} \times 100 \\
& \text { Loss } \%=\frac{\text { Loss }}{\text { Cost price }} \times 100
\end{aligned}\)
Now
0.28 a= 1820/5000
0.28a=36.4*100
Essentially, 3640 is our overall profit but we need to depurate it from the 1820 which is also the 28% +42% profits. Therefore, it is inflated.
3640-1820=2020 which is B
Alternative approach
By inspection , we do not know car 1 initial cost or car 2. we only know that 5000 is the over all cost of both.
Now, if we have a 28% profit on the first one, it is reasonable to conceive that car 1 is the cheaper. Even if you assume that car 1 cost is 2000, the profit of 28% on 2000 is 2560.
therefore, an educated guess is surely B
