Question : A shopkeeper lists the price of an article as Rs. 500. But he gives a certain discount which allows the buyer to pay Rs. 500 for the article including 10% sales tax. The rate of discount is:
Option 1: $10$%
Option 2: $10\frac{1}{11}$%
Option 3: $9\frac{1}{11}$%
Option 4: $12$%
Correct Answer: $9\frac{1}{11}$%
Solution :
Given: A shopkeeper lists the price of an article as Rs. 500.
The sales tax on the Selling Price is 10%.
Let the Selling Price be $x$.
So, $\frac{110x}{100}=500$
⇒ $x=\frac{5000}{11}$
Discount = $500-\frac{5000}{11}=\frac{500}{11}$
So, discount percentage is $\frac{\frac{500}{11}}{500}×100=\frac{100}{11}=9\frac{1}{11}$%
Hence, the correct answer is $9\frac{1}{11}$%.
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