Question

If the selling price of 10 pens is equal to the cost price of 14 pens. Find the gain percent.

Answer 1

Hint: Here S.P. and C.P. of pens are equated but in different quantity First we will find the ratio of cost price and selling price that will help us in finding profit and we will proceed towards finding percentage profit.

Complete step by step answer:

It is given that S.P. of 10 pens = C.P. of 14 pens
Thus we can write
\[\begin{gathered}
  S.P. \times 10 = C.P. \times 14 \\
   \Rightarrow \dfrac{{S.P.}}{{C.P.}} = \dfrac{{14}}{{10}} \\
\end{gathered} \]
Now we can say S.P. = 14 and C.P. =10
\[\begin{gathered}
  \% profit = \dfrac{{profit}}{{C.P.}} \times 100 \\
   \Rightarrow \% profit = \dfrac{{S.P. - C.P.}}{{C.P.}} \times 100 \\
\end{gathered} \]
Placing the values we will find the percent gain/profit.
\[
   \Rightarrow \% profit = \dfrac{{14 - 10}}{{10}} \times 100 \\
   \Rightarrow \% profit = \dfrac{4}{{10}} \times 100 \\
   \Rightarrow \% profit = 40\% \\
    \\
 \]
Thus the gain percent is 40%.

Note: Here selling and cost price is not given directly. So don’t get confused. Don’t even consider selling price at 10 and cost price as 14. Using the ratio method saves your time and it is easy to understand.
Additional information: The price at which the product is bought is called cost price.
It is denoted by C.P. The price at which the product I sold is called the selling price. It is denoted by S.P. If S.P. > C.P., it is a profitable transaction. Profit is given by S.P.-C.P. If S.P < C.P., it is a loss transaction. Loss is given by C.P.-S.P.