Question : A shopkeeper sells his goods at an 18% discount and still earns a 30% profit. If he sells his goods at a 12% discount on the marked price, then what will be his profit percentage (correct to 2 decimal places)?
Option 1: 42.62%
Option 2: 35.45%
Option 3: 40.35%
Option 4: 39.51%
Correct Answer: 39.51%
Solution :
Profit gained by shopkeeper = 30%
Discount% given on the table = 18%
Let the cost price of the table be $a$.
Selling price = $\frac{100 + \text { Profit %}}{100}×$ cost price
Since he gains a profit of 30%, the Selling Price = $\frac{130}{100}a = 1.3a$
Let the Marked Price of the table be $b$.
After 18% discount,
Selling price = $\frac{100 - \text {Discount %}}{100}×$ marked price
⇒ $b - \frac{18}{100} \times b = 1.3a$
⇒ $0.82b = 1.3a$
Now, if he sells the table at $12$% discount,
New selling price will be $= b - (b)\times(\frac{12}{100})=0.88b$
$= 0.88\times \frac{1.3}{0.82}a=1.3951a$
$\therefore$ New profit percent $= \frac{(1.3951a - a)}{a}\times 100 = 39.51$%
Hence, the correct answer is 39.51%.
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