Question : A shopkeeper allows a 20 percent discount on the marked price of an article and he suffers a loss of 5 percent. If the article is sold at marked price, then what will be the profit percentage?
Option 1: 8.33 percent
Option 2: 16.25 percent
Option 3: 18.75 percent
Option 4: 17.25 percent
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Correct Answer: 18.75 percent
Solution :
Here, MP denotes the marked price, CP denotes the cost price.
Discount = 20%
Loss = 5%
$\frac{\text{MP}}{\text{CP}} = \frac{(100-\text{Loss})}{(100-\text{Discount})}$
⇒ $\frac{\text{MP}}{\text{CP}} = \frac{(100-5)}{(100-20)}$
⇒ $\frac{\text{MP}}{\text{CP}} = \frac{95}{80}= \frac{19}{16}$
If there is no discount, means discount = 0%, then profit %
$\frac{\text{MP}}{\text{CP}} = \frac{(100+\text{Profit})}{(100-\text{Discount})}$
⇒ $\frac{19}{16} = \frac{(100+\text{Profit})}{(100-0)}$
⇒ $\frac{19}{16} = \frac{(100+\text{Profit})}{100}$
⇒ $19\times{100}=16(100+\text{Profit})$
⇒ $1900 = 1600 + 16\times{\text{Profit%}}$
⇒ $16\times{\text{Profit%}} = 1900-1600=300$
⇒ $\text{Profit %} = 18.75\%$
Hence, the correct answer is 18.75 percent.
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