Question : A shopkeeper sold an item at 10% loss after giving a discount equal to half the marked price. Then the cost price is:
Option 1: $\frac{1}{9}$th of the marked price
Option 2: $\frac{4}{9}$th of the marked price
Option 3: $\frac{5}{9}$th of the marked price
Option 4: $\frac{7}{9}$th of the marked price
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Correct Answer: $\frac{5}{9}$th of the marked price
Solution :
Let the marked price = $p$ and the cost price = $q$
According to the question,
∴ 50% of $p$ = 90% of $q$
⇒ $\frac{p×50}{100}=\frac{q×90}{100}$
∴ $q=\frac{5}{9}p$
So, the cost price is $\frac{5}{9}$th of the marked price.
Hence, the correct answer is $\frac{5}{9}$th of the marked price.
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