Question

Sam purchased 20 dozens of toys at the rate of $ {\rm{Rs}}{\rm{.}}\;{\rm{375}} $ per dozen. He sold each one of them at the rate of $ {\rm{Rs}}{\rm{.}}\;{\rm{33}} $ . What was his percentage profit?

Answer 1

Hint: To find the gain percentage, we will firstly find the cost price of 1 toy from the cost price of 1 dozen toys. Then we will find profit by finding the difference between cost price and selling price of the toy. After that, we substitute the values of cost price and profit in the expression of profit percentage to find its percentage.

Complete step-by-step answer:
 Given:
The cost price of 1 dozen of toys is $ {\rm{Rs}}.\;375 $ .
The selling price of 1 toy is $ {\rm{Rs}}.\;33 $ .
We will find the cost price of 1 dozen of the toys by dividing the cost price of 1 dozen of toys by 12. This can be expressed as:
 $ \begin{array}{l}
{\rm{C}}{\rm{.P}}{\rm{.}} = {\rm{Rs}}.\left( {\dfrac{{375}}{{12}}} \right)\\
{\rm{C}}{\rm{.P}}{\rm{.}} = {\rm{Rs}}.\,31.25
\end{array} $
 From the question we know that the selling price of the one toy is $ {\rm{Rs}}.\;33 $ . This can be expressed as:
 $ {\rm{S}}{\rm{.P}}{\rm{.}} = {\rm{Rs}}{\rm{.}}\;33 $
 We know that in order to find profit we will find the difference between the cost price $ \left( {{\rm{C}}{\rm{.P}}{\rm{.}}} \right) $ and selling price $ \left( {{\rm{S}}{\rm{.P}}{\rm{.}}} \right) $ of 1 toy. This can be expressed as:
\[{\rm{Profit}} = {\rm{S}}{\rm{.P}}. - {\rm{C}}{\rm{.P}}.\]
 We will substitute $ {\rm{Rs}}.\,31.25 $ for $ {\rm{C}}{\rm{.P}}{\rm{.}} $ and $ {\rm{Rs}}.\;33 $ for $ {\rm{S}}{\rm{.P}}{\rm{.}} $ in the above expression.
\[\begin{array}{l}
{\rm{Profit}} = {\rm{Rs}}.\;33 - {\rm{Rs}}.\,31.25\\
{\rm{Profit}} = {\rm{Rs}}.\;1.75
\end{array}\]
 We will use the expression of profit percentage which can be expressed as:
 $ {\rm{Profit}}\% = \dfrac{{{\rm{Profit}}}}{{{\rm{C}}{\rm{.P}}{\rm{.}}}} \times 100 $
 Now, we will substitute $ {\rm{Rs}}.\,31.25 $ for $ {\rm{C}}{\rm{.P}}{\rm{.}} $ and \[{\rm{Rs}}.\;1.75\] for profit in the above expression.

 $ \begin{array}{l}
{\rm{Profit}}\% = \dfrac{{{\rm{Rs}}.\;1.75}}{{{\rm{Rs}}.\,31.25}} \times 100\\
{\rm{Profit}}\% = \dfrac{{28}}{5}\% \\
{\rm{Profit}}\% = 5.6\%
\end{array} $
 Sam’s gain percentage is $ 5.6\% $ .

Note: To find the gain percentage in this problem, we should have prior knowledge about the formulas of the profit and profit percentage. The data 20 dozens are redundant data since it is not used in the calculation. In this question, it was mentioned that we need to find the profit percentage, but if in other problems it is not given in the question, then we can check for the cost price and selling price of the object. If the selling price is greater than the cost price, then we earn a profit, but if the selling price is less than the cost price, we will suffer loss.