Question : A shopkeeper sells a table at a discount of 20 percent and earns a profit of 30 percent. If he sells the same table at a 10 percent discount, then what will be his new profit or loss percent?
Option 1: 32.5 percent profit
Option 2: 40.5 percent loss
Option 3: 46.25 percent profit
Option 4: 50.5 percent loss
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Correct Answer: 46.25 percent profit
Solution :
Let the marked price be Rs. 100.
After a 20% discount, the selling price is 80% of 100 = Rs. 80
This is also the cost price with 30% profit, so 80 = 1.3 $\times$ (cost price)
⇒ Cost price = $\frac{80}{1.3}$
Now, the selling price with a 10% discount is 90% of 100 = 90.
⇒ Profit = Selling price – Cost price $= 90 - \frac{80}{1.3}=\frac{117 - 80}{1.3}=\frac{37}{1.3}$
⇒ Profit % = $\frac{\frac{37}{1.3}}{\frac{80}{1.3}} × 100=\frac{37}{80} × 100= 46.25\%$
Hence, the correct answer is 46.25 percent profit.
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