Question

A retailer sells an article for Rs. $5,350$ including $7\%$ Sales Tax on the listed price. If he had bought it at a discount and has made a profit of $25\%$ on the whole, find the rate of discount he gets.

• A. $14.4\%$
• B. $17.4\%$
• C. $16.4\%$
• D. None of these

Answer 1

The correct option is D None of these

Let the listed price of the article is Rs. x and discount is d%

The selling price of the article $=Rs.5350$

$\therefore x+7\%$ of $x=5350$

$\Rightarrow x+\frac{7x}{100}=5350$

$\Rightarrow \frac{107x}{100}=5350$

$\Rightarrow 107x=5350\times 100$

$\Rightarrow x=\frac{5350\times 100}{107}=Rs.5000$

$\therefore Listprice=Rs.5000$

The cost price of the article to the retailer $=5000-d$

$\Rightarrow 5000(1-\frac{d}{100})$

$\Rightarrow 50(100-d)$

Profit to the retailer $=5350-50(100-d)=Rs.(350+50d)$

$Profit\%=\frac{Profit}{C.P}\times 100$

$\Rightarrow 25=\frac{(350+50d)}{50(100-d)}\times 100$

$\Rightarrow 100-d=4(7+d)$

$\Rightarrow 100-d=28+4d$

$\Rightarrow 5d=100-28$

$\Rightarrow 5d=72$

$\Rightarrow d=\frac{72}{5}=14.4\%$

Thus the rate of discount is $14.4\%$