Question

A shopkeeper expects a gain of $\dfrac{{45}}{2}\% $ on his C.P. If his sale was Rs. 392, then find his profit.

Answer 1

Hint: To find the profit from the profit percent$\dfrac{{45}}{2}\% $ and the sale price Rs. 392 of the product first, we have to find the cost price of the product by the formula of cost price. After finding the cost price use the profit formula to find the profit of the shopkeeper.

Complete step-by-step answer:
It is given that:
Selling Price of the product$ = {\rm{Rs}}.\;392$
Shopkeeper expect the profit%$ = \dfrac{{45}}{2}\% $
We know that the formula for the selling price is
${\rm{Selling\;Price}} = \left( {\dfrac{{100 + {\rm{profit\;percent}}}}{{100}} \times {\rm{Cost\;price}}} \right)$
In this solution, we have to give the selling price and we have to find the cost price, so use cross multiplication in the above expression.
Then, the formula becomes,
${\rm{Cost\;Price}} = \left( {\dfrac{{{\rm{Selling\;Price}} \times 100}}{{100 + {\rm{profit\;percent}}}}\;} \right)$
Substituting the value 392 for selling price and $\dfrac{{45}}{2}$ for the profit percent in the above formula:
${\rm{Cost\;Price}} = \left( {\dfrac{{392 \times 100}}{{100 + \dfrac{{45}}{2}}}\;} \right)$
Simplify the above expression, to find the value of cost price.
$\begin{array}{c}{\rm{Cost\;Price}} = \left( {\dfrac{{39200}}{{100 + 22.5}}\;} \right)\\ = \left( {\dfrac{{39200}}{{122.5}}\;} \right)\\ = 320\end{array}$

Therefore, the cost price of the product is ${\rm{Rs}}{\rm{. }}320$.
We know that, the formula for the profit is:
${\rm{Profit}} = {\rm{Selling\;Price}} - {\rm{Cost\;Price}}$

Substituting the value 392 for selling price and 320 for the cost price in the above formula.
$\begin{array}{c}{\rm{Profit}} = 392 - 320\\ = 72\end{array}$

Therefore, the profit of the shopkeeper is about Rs.72.

Note:
In this solution, the cost price is used to find the profit of the shopkeeper and we can find the profit if the selling price is greater than the cost price. Also, in this solution, we can calculate the profit of the shopkeeper because the selling price is greater than the cost price.