Question : A 45% profit is made when a discount of 45% is given on the marked price of an item. If the discount on the marked price of the same item is 50%, then the profit will be:
Option 1: $31 \frac{9}{11}$%
Option 2: $33 \frac{2}{11}$%
Option 3: $30\frac{7}{11}$%
Option 4: $31\frac{7}{11}$%
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Correct Answer: $31 \frac{9}{11}$%
Solution : Let the marked price be $100x$. Discount = 45% Selling price $= 100x - \frac{45}{100} \times 100x = 55x$ Profit percentage = 45% Cost price $= \text{Selling price} \times \frac{100}{100 + \text{Profit}\%}$ ⇒ Cost price $= 55x \times \frac{100}{100 + 45}$ ⇒ Cost price $= \frac{5500}{145}x$ New selling price $= 100x - \frac{50}{100} \times 100x = 50x$ Profit $= 50x - \frac{5500}{145}x = \frac{1750}{145}x$ $\therefore$ Profit % $=\frac{\frac{1750}{145}x}{\frac{5500}{145}x} \times 100 = 31\frac{45}{55} = 31\frac{9}{11}$% Hence, the correct answer is $31\frac{9}{11}$%.
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