Question

In a certain store, the profit is \[{\text{32}}0\% \] of the cost. If the cost increases by \[{\text{2}}5\% \] but the selling price remains constant approximately. What percentage of the selling price is the profit?

Answer 1

Hint: - In this question we have to find a numeric relation between selling price and profit and to find profit we need selling price and cost price, so according to given data firstly we will find selling price and cost price.


Complete step by step solution
We all know that cost price is the price at which we buy a thing and selling price is the price
At which we sell a thing.
We have given that profit is \[{\text{32}}0\% \] of cost price
Let the cost price be \[100x\].
Then according to question profit is
\[\begin{gathered}
  100 \times 320\% = {\text{ }}100 \times \dfrac{{320}}{{100}} \\
   = 320x \\
\end{gathered} \]
Now selling price = cost price + profit
\[\begin{gathered}
   = 100x + 320x \\
   = 420x \\
\end{gathered} \]
If the cost price increases by\[{\text{2}}5\% \], then the new cost price will be
New Cost Price
$\begin {gathered}
  100x + 100x \times \dfrac{{25}}{{100}} \\
   = 100x + 25x \\
   = 125x \\
\end{gathered} $
Now in this condition profit is
Profit= selling price - cost price
$\begin{gathered}
   = 420x - 125x \\
   = 295x \\
\end{gathered} $
We have to find profit is what percent of selling price
$\begin{gathered}
   \Rightarrow \dfrac{{295x}}{{420x}} \times 100 \\
   \Rightarrow \dfrac{{29500}}{{420}} \\
   \Rightarrow 70\% (Approximately) \\
\end{gathered} $


Note – In a profitable deal selling prices is more than cost price, so in order to find profit value, subs-tract cost price from selling price, not selling price from cost price, otherwise profit will be negative.