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

$70\%$

Explanation for the correct answer:

Finding the new profit percentage:

Let the cost price be $x$.

Profit$=320\%ofx$

$\Rightarrow$Profit$=\frac{320}{100}\times x$

$\Rightarrow$Profit$=3.2x$$...\left(i\right)$

Selling price $=$Cost price$+$ profit

$\Rightarrow$Selling price $=$$x+3.2x=4.2x$$...\left(ii\right)$

Now cost price is increased by $25\%$

$\Rightarrow$New cost price$=125\%$ of cost price

$\Rightarrow$New cost price$=1.25x$

Hence, revised profit $=$Selling price $-$ New cost price

$\Rightarrow$ revised profit $=$$4.2x-1.25x=2.95x$$...\left(iii\right)$

Profit expressed as percentage of selling price is given as

Required percentage $=\frac{revisedprofit}{sellingprice}\times 100$

$\Rightarrow$Required percentage $=\frac{2.95x}{4.2x}\times 100$

$\Rightarrow$Required percentage $=70.23\%\approx 70\%$$...\left(iv\right)$

Hence, profit expressed as percentage of selling price is approximately $70\%$,

Hence, option(C) is the correct answer.