Question

A trader bought some goods at a discount of 20% of the list price. He wants to mark them at such a price that he can give a discount of 20% on the marked price and still make a profit of 25%. Find the percent of the list price at which he should mark the goods.

• A. 25% above the list price
• B. 15% below the list price
• C. 25% below the list price
• D. 15% above the list price

Answer 1

The correct option is A 25% above the list price

Let the list price be $Rs.x$

Cost price $=20\%$ discount on the list price

That will be $80\%$ of the list price

$CostPrice=\frac{(80\times x)}{100}$

$CostPrice=\frac{4x}{5}$

The profit is $25\%$ on the selling price.

So, selling price $=125\%$ of the cost price.

$=\frac{125}{100}\times \frac{4x}{5}$

$=x$

Let the marked price be $Rsy$

If the merchant gives $20\%$ discount,

Then $80\%$ of marked price = Selling price

$⟹\frac{80y}{100}=x$

After cross multiplying, we get.

$100x=80y$

$y=\frac{5x}{4}$

The percentage of the list price at which the merchant marks the goods

$=\frac{(MarkedPrice-ListPrice)100}{ListPrice}$

$=\frac{(y-x)100}{x}$

$=\frac{(\frac{5x}{4}-x)100}{x}=\left(\frac{(5x-4x)\times 100}{4x}\right)=25\%$

Hence the price should be $25\%$ above the list price.