Question

A shopkeeper allows '$20\%$' off on the marked price of goods and still gets a profit of $25\%$. What is the actual cost to him of an article marked $₹500$?

Answer 1

Given: Profit$=25\%$, Marked Price(M.P.)$=₹500$, and Discount$=20\%$

Here, we have to determine the actual cost to him of an article.

$\Rightarrow$Discount$=\frac{\mathrm{M}.\mathrm{P}.\times \mathrm{Discount}\%}{100}$

$=\frac{500\times 20}{100}$

$=₹100$

$\Rightarrow \mathrm{Selling}\mathrm{Price}(\mathrm{S}.\mathrm{P}.)=\mathrm{M}.\mathrm{P}.-\mathrm{Discount}$

$=500-100$

$=₹400$

And $25\%$ profit he gets additionally,

From the formula, we know that

$\mathrm{Cost}\mathrm{Price}(\mathrm{C}.\mathrm{P}.)=\frac{100}{100+\mathrm{Gain}\%}\times \mathrm{S}.\mathrm{P}.$

$=\frac{100}{100+25}\times 400$

$=\frac{100}{125}\times 400$

$=₹320$

Therefore, the actual cost of the article is $₹320$.