Question : A shopkeeper sells a table at a $25\%$ discount on the marked price and earns a profit of $70\%$. If he sells the same table at $50 \%$ discount, then his new profit percentage will be:
Option 1: $11 \frac{1}{3} \%$
Option 2: $12 \frac{1}{2} \%$
Option 3: $13 \frac{1}{3} \%$
Option 4: $13 \frac{1}{2} \%$
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Correct Answer: $13 \frac{1}{3} \%$
Solution :
Let the marked price be $100$.
The discount is $25$% on the Marked Price.
So, the selling price = $100 - 25 = 75$
Profit is $70$%.
Cost price = $\frac{100}{170}×75=\frac{750}{17}$
If he sells the same table at $50 \%$ discount,
New selling price = $100 -50 = 50$
New profit = New selling price – Cost price
⇒ New profit = $50-\frac{750}{17}=\frac{100}{17}$
So, new profit percentage = $\frac{\text{New profit}}{\text{Cost price}}×100$
= $\frac{\frac{100}{17}}{\frac{750}{17}}×100$
= $13\frac{1}{3}$%
Hence, the correct answer is $13 \frac{1}{3} \%$.
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