Question : When a discount of 20% is given on a sweater, the profit is 28%. If the discount is 14%, then the profit is:
Option 1: 42%
Option 2: 46.4%
Option 3: 33.2%
Option 4: 37.6%
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Correct Answer: 37.6%
Solution :
Let the cost price of the sweater be Rs. 100 and its marked price is Rs. $x$.
Use: Selling Price = Marked price × $\frac{100 - \text{Discount}\ \%}{100}$ and Profit % = $\frac{\text{Selling Price – Cost Price}}{\text{Cost Price}}×100$
According to the question,
⇒ $\frac{x \times 80}{100} =128$
⇒ $\frac{x \times 4}{5}= 128$
⇒ $x =\frac{128 \times 5}{4}=160$
When discount = 14%, then,
Selling price of sweater = 160 × (100 – 14)% = $\frac{160 \times 86}{100}$ = Rs. 137.6
$\therefore$ Profit percentage = 137.6 – 100 = 37.6%
Hence, the correct answer is 37.6%.
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