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A selling price of 10 pens is equal to the cost price of 14 pens, find his gain(in percent).

Answer
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Hint: We will assume x as the selling price of 10 pens and cost price of 14 pens will also be x. Then, we will find the SP and CP of 1 pen. Then, we will use the fact that gain is equal to selling price minus cost price, i.e. gain= S.P. -C.P. We will use the formula, $gain\%=\dfrac{gain}{C.P}\times 100$ to get the gain%.

Complete step by step answer:
Let us take the selling price (S.P.) of 10 pens to be Rs. x.
Now, from this we can say that the S.P. of 1 article is
\[=Rs.\ \dfrac{x}{10}\]
Now, as given in the question, we know that the cost price(C.P.) of 14 pens is also Rs. x.
So, from this, we can get the C.P. of 1 article is
\[=Rs.\ \dfrac{x}{14}\]
Now, the profit made by selling 10 pens can be calculated as follows
Profit=selling price of 10 pens -cost price of 10 pens
 Profit=x-10 times the cost price of 1 pens
(As assumed at the start of the question)
\[\begin{align}
  & =x-10\times \dfrac{x}{14} \\
 & =\dfrac{4x}{10} \\
 & =\dfrac{2x}{5} \\
\end{align}\]
Hence, this is the profit that is experienced.
Now, for the profit percent, we can use the formula that is given in the hint as follows
\[\begin{align}
  & \Rightarrow profit\%=\dfrac{profit}{C.P.}\times 100 \\
 & \Rightarrow profit\%=\dfrac{\dfrac{2x}{5}}{10\times \dfrac{x}{14}}\times 100 \\
 & \Rightarrow profit\%=\dfrac{14}{25}\times 100\% \\
 & \Rightarrow profit\%=52\% \\
\end{align}\]

Hence the profit percentage = 52%

Note: Another method of doing this question is that we could simply take the cost price of 1 pen 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.