Question : A shopkeeper sells a table at a discount of 20% and earns a profit of 60%. If he sells the same table at a 40% discount, then what will be his new profit percentage?
Option 1: 20
Option 2: 30
Option 3: 35
Option 4: 40
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Correct Answer: 20
Solution :
Profit gained by shopkeeper = 60%
Discount% given on the table = 20%
Let the cost price of the table be $a$.
Since, he gains a profit of 60%, the selling price = $a + \frac{60}{100}a = 1.6a$
Let the marked price of the table be $b$.
After 20% discount,
$b - \frac{20}{100} \times b = 1.6a$
⇒ $b = 2a$
Now, if he sells the table at $40$% discount,
New selling price will be $ = 2a - (2a)\times(\frac{40}{100})$
New selling price $ = 1.2a$
$\therefore$ New profit percent $= [\frac{1.2a - a}{a}]\times 100 = 20$%
Hence, the correct answer is 20.
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