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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.

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