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Let us take the selling price (S.P.) of 9 articles to be Rs. x.

Now, from this we can say that the S.P. of 1 article is

\[=Rs.\ \dfrac{x}{9}\]

Now, as given in the question, we know that the cost price(C.P.) of 10 articles is also Rs. x.

So, from this, we can get the C.P. of 1 article is

\[=Rs.\ \dfrac{x}{10}\]

Now, the profit made by selling 9 articles can be calculated as follows

Profit=selling price of 9 articles -cost price of 9 articles

Profit=x-9 times the cost price of 1 articles

(As assumed at the start of the question)

\[\begin{align}

& =x-9\times \dfrac{x}{10} \\

& =\dfrac{x}{10} \\

& =\dfrac{x}{10} \\

\end{align}\]

Hence, this is the profit that is experienced.

Now, for the profit percent, we can use the formula that is as follows,

\[\begin{align}

& \Rightarrow profit\%=\dfrac{profit}{C.P.}\times 100 \\

& \Rightarrow profit\%=\dfrac{\dfrac{x}{10}}{9\times \dfrac{x}{10}}\times 100 \\

& \Rightarrow profit\%=\dfrac{1}{9}\times 100\% \\

& \Rightarrow profit\%=11.11\% \\

\end{align}\]

Then, we can proceed further as directed in the question and then we can use the formula for finding the profit % to get the final answer which would be the same as this one. Also, some students may make mistakes while writing the formula of profit percentage and may write SP instead of CP in the formula, so this must be avoided.

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