Question

Pens are bought at a \[12\] for a rupee and sold at \[9\] for a rupee. Find the gain or loss \[\%\].

Answer 1

Hint: In order to find the gain or loss \[\%\], we must find the cost price and selling price of one pen firstly. Then we must compare them and decide if loss occurs or gain occurs. After finding that out, we must calculate the percent of either loss or gain and that will be our required answer.

Complete step-by-step solution:
Now let us learn about selling price and cost price. The price at which a good is being bought is considered as cost price. In the same way, the price at which the good is being sold is called the selling price. While comparing the cost price and selling price, if the cost price is greater than the selling price, then loss occurs. If the selling price is greater than the cost price, then gain or profit occurs.
Now let us find the gain or loss \[\%\].
Firstly, let us find the cost price and selling price of one pen.
We are given that the cost of \[12\] pens is \[1Rupee\] and the selling price of \[9\] pens is \[1Rupee\].
Cost price of one pen\[=\dfrac{1}{12}\]
Selling price of one pen\[=\dfrac{1}{9}\]
Upon comparing, we can observe that selling price is greater than cost price. So gain occurs.
Now let us calculate the gain and the gain percent. We get,
\[gain=SP-CP\]
\[\Rightarrow \dfrac{1}{9}-\dfrac{1}{12}=\dfrac{4-3}{36} =\dfrac{1}{36}\]
We get the profit as \[Rs.\dfrac{1}{36}\].
Now let us calculate the gain percent. We get,
\[gain\%=\dfrac{gain}{CP}\times 100=\dfrac{\dfrac{1}{36}}{\dfrac{1}{12}}\times 100=33.3\%\]
\[\therefore \] The gain percent is \[33.3\%\].

Note: We must have a note that the cost price or the selling price can never be negative. In order to remove the negative nature, we will be applying mod to the value which converts into positive. We can apply this loss or gain percent in everyday life to calculate them.