Question

# The cost price of 10 articles is equal to the selling price of 9 articles. Find the profit percent.

Hint: We will assume the selling price of 9 articles as x so we will also get the cost price of 10 articles as x, and then we will find the selling price of 1 article and also the cost price of 1 article. We will then find the profit as profit = SP - CP. Using these values we will find the profit percentage, which is given by $gain\%=\dfrac{gain}{C.P}\times 100$ .

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}

Hence we get the profit percentage = 11.11%

Note: Another method of doing this question is that we could simply take the cost price of 1 article to be Re. 1.
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.