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Eddy bought a bicycle at discount for $Y from ranger bicycles. But he
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03 Jun 2025, 02:13
03 Jun 2025, 02:13
Expert Reply
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Question Stats:
40% (01:50) correct
60% (00:49) wrong based on 5 sessions
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Eddy bought a bicycle at discount for $Y from ranger bicycles. But he sold it to his friend at the initial marked price, thereby making 20% profit on purchase price.
Quantity A |
Quantity B |
Discount percentage offered by ranger bicycles to Eddy |
20% |
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Re: Eddy bought a bicycle at discount for $Y from ranger bicycles. But he
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03 Jun 2025, 10:43
03 Jun 2025, 10:43
1
Let marked price = c
Sold bicycle to friend at a discount of $y therefore
Cost price = c - y
Selling price = c
Profit = c - y/5
Since SP = CP + P
c = c - y + c - y/5
c = 5c -5y+ c - y/5
c = 6y
Discount % = discount /marked price X 100
y/c X 100
y/6y X 100
= 100/6
16.6666%
Answer choice B
Sold bicycle to friend at a discount of $y therefore
Cost price = c - y
Selling price = c
Profit = c - y/5
Since SP = CP + P
c = c - y + c - y/5
c = 5c -5y+ c - y/5
c = 6y
Discount % = discount /marked price X 100
y/c X 100
y/6y X 100
= 100/6
16.6666%
Answer choice B
Re: Eddy bought a bicycle at discount for $Y from ranger bicycles. But he
[#permalink]
05 Jun 2025, 04:00
05 Jun 2025, 04:00
Expert Reply
Let the initial marked price of the bicycle be $M$.
Eddy bought the bicycle at a discount for $Y$. So, Eddy's purchase price is $Y$.
Eddy sold the bicycle to his friend at the initial marked price, $M$.
He made a $20 \%$ profit on his purchase price.
This means his selling price $(M)$ is his purchase price $(Y)$ plus $20 \%$ of his purchase price.
$$
\(\begin{aligned}
M & =Y+0.20 Y \\
M & =1.20 Y
\end{aligned}\)
$$
We want to find the discount percentage offered by Ranger Bicycles to Eddy.
The discount is the difference between the initial marked price and the price Eddy paid.
Discount amount $=M-Y$
Discount percentage $\(=\frac{\text { Discount amount }}{\text { Initial marked price }} \times 100 \%\)$
Discount percentage $\(=\frac{M-Y}{M} \times 100 \%\)$
Substitute $\(M=1.20 Y\)$ into the discount percentage formula:
Discount percentage $\(=\frac{1.20 Y-Y}{1.20 Y} \times 100 \%\)$
Discount percentage $\(=\frac{0.20 Y}{1.20 Y} \times 100 \%\)$
Discount percentage $\(=\frac{0.20}{1.20} \times 100 \%\)$
Discount percentage $\(=\frac{2}{12} \times 100 \%\)$
Discount percentage $\(=\frac{1}{6} \times 100 \%\)$
Discount percentage $\(=16.66 \ldots \%\)$
Compare Quantity A and Quantity B:
- Quantity A: Discount percentage offered by Ranger Bicycles to Eddy $\approx 16.67 \%$
- Quantity B: $20 \%$
Since $\(16.67 \%<20 \%\)$, Quantity $\(B\)$ is greater.
The final answer is $B$
Eddy bought the bicycle at a discount for $Y$. So, Eddy's purchase price is $Y$.
Eddy sold the bicycle to his friend at the initial marked price, $M$.
He made a $20 \%$ profit on his purchase price.
This means his selling price $(M)$ is his purchase price $(Y)$ plus $20 \%$ of his purchase price.
$$
\(\begin{aligned}
M & =Y+0.20 Y \\
M & =1.20 Y
\end{aligned}\)
$$
We want to find the discount percentage offered by Ranger Bicycles to Eddy.
The discount is the difference between the initial marked price and the price Eddy paid.
Discount amount $=M-Y$
Discount percentage $\(=\frac{\text { Discount amount }}{\text { Initial marked price }} \times 100 \%\)$
Discount percentage $\(=\frac{M-Y}{M} \times 100 \%\)$
Substitute $\(M=1.20 Y\)$ into the discount percentage formula:
Discount percentage $\(=\frac{1.20 Y-Y}{1.20 Y} \times 100 \%\)$
Discount percentage $\(=\frac{0.20 Y}{1.20 Y} \times 100 \%\)$
Discount percentage $\(=\frac{0.20}{1.20} \times 100 \%\)$
Discount percentage $\(=\frac{2}{12} \times 100 \%\)$
Discount percentage $\(=\frac{1}{6} \times 100 \%\)$
Discount percentage $\(=16.66 \ldots \%\)$
Compare Quantity A and Quantity B:
- Quantity A: Discount percentage offered by Ranger Bicycles to Eddy $\approx 16.67 \%$
- Quantity B: $20 \%$
Since $\(16.67 \%<20 \%\)$, Quantity $\(B\)$ is greater.
The final answer is $B$
