Question : A dealer gains 20% by selling an article at 25% discount on its marked price. If the cost price of the article is decreased by 15%, how much discount percentage should he now give on the same marked price so as to earn the same percentage of profit as before?
Option 1: 32.50%
Option 2: 35%
Option 3: 36.25%
Option 4: 37.75%
Correct Answer: 36.25%
Solution :
Let the cost price of the article be $100x$.
Selling price = $100x × \frac{6}{5} = 120x $
Marked price = $120x × \frac{4}{3} = 160x $
New cost price = $100x × \frac{85}{100} = 85x $
New selling price = $85x × \frac{6}{5} = 102x$
Let the discount percentage be $a\%$.
Now,
$102x = 160x × \frac{(100 - a)}{100}$
⇒ $10200x = 16000x - 160ax$
⇒ $160ax = 5800x$
⇒ $a = \frac{5800x}{160x}$
⇒ $a = 36.25$
Hence, the correct answer is 36.25%.
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