Question

In a certain store, the profit is $320\%$of the cost. If the cost increases by $25\%$but the selling price remains constant, approximately what percentage of the selling price is the profit?

• A. $30\%$
• B. $100\%$
• C. $70\%$
• D. $250\%$

Answer 1

The correct option is C

$70\%$

The explanation for the correct option.

Step 1: Find Selling Price.

Given: Profit $=320\%$

Let the cost price be $100$.

Then, profit is

$$\begin{gathered} =320\%\mathrm{of}100[\mathrm{Profit}=\mathrm{Profit}\%\mathrm{of}\mathrm{CP}] \\ =\frac{320}{100}\times 100 \\ =320 \end{gathered}$$

The selling price of the product $=320+100\mathbf{}\mathbf{}[\mathrm{SP}=\mathrm{CP}+\mathrm{Profit}]$

$=420$

Step 2: Calculate the new cost price.

New Cost Price increased by $25\%$

So, New Cost price $=100+25\%\mathrm{of}100$

$$\begin{gathered} =100+\frac{25}{100}\times 100 \\ =100+25 \\ =125 \end{gathered}$$

Step 3: Calculate the new profit $\%$

Selling Price$=420$

New Profit is $420-125=295\mathbf{}[\mathrm{Profit}=\mathrm{SP}-\mathrm{CP}]$

$$\begin{gathered} \mathrm{Profit}(\%)=\frac{\mathrm{Profit}}{\mathrm{SP}}\times 100 \\ =\frac{295}{420}\times 100 \\ =70.2\% \end{gathered}$$

Hence, option (C) is correct.