Question : A trader gains 25% by selling an article with a 20% discount on its marked price. If the cost price of the article increases by 30%, then how much discount (in %) should he offer on the same marked price to gain 15% of profit?
Option 1: 4.32%
Option 2: 5.08%
Option 3: 5.12%
Option 4: 4.87%
Correct Answer: 4.32%
Solution :
Let the marked price of the article be 100.
The trader gives a 20% discount on its marked price.
So, the selling price = 100 – 20 = 80
He gains 25%.
$\therefore$ Cost price of the article $=\frac{100}{100+25}×80=\frac{100}{125}×80=64$
Now, the cost price of the article increases by 30%.
New cost price $=\frac{100+30}{100}×64=\frac{130}{100}×64=83.2$
To gain 15% of profit, the selling price must be $=\frac{100+15}{100}×83.2=\frac{115}{100}×83.2=95.68$
So, the discount percentage on marked price $=\frac{100-95.68}{100}×100=\frac{4.32}{100}×100=4.32\%$
Hence, the correct answer is 4.32%.
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