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If a person had purchased $11$ articles for Rs.$10$ and sold all the articles at the rate of Rs.$11$ for $10$ the profit percent would have been
(A) $10\% $
(B) $11\% $
(C) $21\% $
(D) $100\% $

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Last updated date: 13th Jun 2024
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Answer
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Hint: Find the cost price and selling price of one article and then find out the profit percent by using the formula, \[Profit\% {\text{ }} = {\text{ }}\dfrac{{Profit}}{{Cost{\text{ }}Price}} \times 100\], where Profit = Selling Price – Cost Price.

Complete step-by-step answer:
Given, cost price of $11$ articles = Rs.$10$
Therefore, cost price of $1$ article = Rs. $\dfrac{{10}}{{11}}$
Also given, selling price of $10$ articles = Rs. $11$
Therefore, selling price of $1$ article = Rs. $\dfrac{{11}}{{10}}$
Since the selling price of $1$ article is greater than the cost price of $1$ article, hence there is a profit.
Profit = Selling Price – Cost Price
$ \Rightarrow $Profit = $\dfrac{{11}}{{10}} - \dfrac{{10}}{{11}}$
$ \Rightarrow $Profit = $\dfrac{{11 \times 11 - 10 \times 10}}{{10 \times 11}}$
$ \Rightarrow $Profit = $\dfrac{{121 - 100}}{{110}}$
$ \Rightarrow $Profit =Rs. $\dfrac{{21}}{{110}}$
Now, we have to calculate the profit percent which is calculated by the formula,
\[Profit\% {\text{ }} = {\text{ }}\dfrac{{Profit}}{{Cost{\text{ }}Price{\text{ }}of{\text{ }}one{\text{ }}article}} \times 100\]
$ \Rightarrow $\[Profit\% {\text{ }} = {\text{ }}\dfrac{{\dfrac{{21}}{{110}}}}{{\dfrac{{10}}{{11}}}} \times 100\]
$ \Rightarrow $\[Profit\% {\text{ }} = {\text{ }}\dfrac{{21 \times 11}}{{110 \times 10}} \times 100\]
$ \Rightarrow $\[Profit\% {\text{ }} = {\text{ }}\dfrac{{21 \times 11}}{{11}}\]
$ \Rightarrow $\[Profit\% {\text{ }} = {\text{ 21% }}\]
Therefore, profit percent is $21% $.

Hence, option (C) is the correct answer.

Note: This question can also be solved by making the no. of articles equal as described below:
 Given, cost price of $11$ articles = Rs.$10$
& selling price of $10$ articles = Rs. $11$
Now making the no. of particles equal by taking LCM of no. of articles.LCM of $11$ and $10$ is $110$.
So, cost price of $110$$\left( { = 11 \times 10} \right)$ articles = $10 \times 10$= Rs. $100$
& selling price of $110$$\left( { = 10 \times 11} \right)$ articles = $11 \times 11$= Rs. $121$
Since selling price is greater than cost price, hence there is a profit.
Profit = Selling Price – Cost Price
$ \Rightarrow $Profit = $121 - 100$
$ \Rightarrow $Profit = Rs. $21$
Now, we have to calculate the profit percent which is calculated by the formula,
\[Profit\% {\text{ }} = {\text{ }}\dfrac{{Profit}}{{Cost{\text{ }}Price}} \times 100\]
$ \Rightarrow $\[Profit\% {\text{ }} = {\text{ }}\dfrac{{21}}{{100}} \times 100\]
$ \Rightarrow $\[Profit\% {\text{ }} = {\text{ 21% }}\]
 Therefore, profit percent is $21% $.
Hence, option (C) is the correct answer.