Question

If a merchant offers a discount of $30\%$ on the list price, then she made a loss of $16\%$. What $\%$ profit or $\%$ loss will she make if she sells at a discount of $10\%$ of the list price?

• A. $6\%$ loss
• B. $0.8\%$ profit
• C. $6.25\%$ loss
• D. $8\%$ profit

Answer 1

The correct option is D $8\%$ profit

Let the cost price of the article be $Rs.100$.
Let the list price of the article be"x".
Then, when the merchant offers a discount of $30\%$, the merchant will sell the article at $x-30\%$ of x $=70\%$ of x $=0.7x........\left(1\right)$
The loss made by the merchant when she offers a discount of $30\%$ is $16\%$.
Therefore, the merchant would have got $100-16\%$ of $100=Rs.84$. when she offered a discount of $30\%......\left(2\right)$
Therefore, equating equations (1) and (2), we get
$0.7x=84$
or $x=120$.
If the list price is $Rs.120$ (our assumption of cost price is $Rs.100$), then when the merchant offers a discount of $10\%$, she will sell the article at
$120-10\%$ of $120=Rs.108$
As the cost price of the article was $Rs.100$ and the merchant gets $Rs.108$ while offering a discount of $10\%$, she will make a profit of $8\%$.