A shopkeeper wants to earn a profit of \(11\frac{1}{9}\%\) even after giving two successive discounts of \(16\frac{2}{3}\%\) and 20% on the marked price of an article. If the cost price of the article for the shopkeeper is ₹1800, what should its marked price be?
₹3000
First find the selling price from the required profit. A profit of \(11\frac{1}{9}\% = \frac{100}{9}\%\) gives \(SP = 1800 \times \left(1 + \frac{1}{9}\right) = 1800 \times \frac{10}{9} = 2000\).
Now relate the selling price to the marked price through the two successive discounts. A discount of \(16\frac{2}{3}\% = \frac{50}{3}\%\) leaves a factor of \(1 - \frac{1}{6} = \frac{5}{6}\).
A discount of 20% leaves a factor of \(1 - \frac{20}{100} = \frac{4}{5}\).
So \(SP = MP \times \frac{5}{6} \times \frac{4}{5} = MP \times \frac{2}{3}\).
Therefore \(2000 = MP \times \frac{2}{3}\), which gives \(MP = 2000 \times \frac{3}{2} = 3000\).
Hence, the marked price should be ₹3000.
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