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Arithmetic
A shopkeeper marks up the price of an article by 50%. He then offers a discount of 20% on the marked price. If the selling price of the article is ₹1200, what was the cost price of the article?\n\nA) ₹900\nB) ₹1000\nC) ₹1100\nD) ₹1250
Correct Option: B\n\nLet the Cost Price (CP) of the article be $\text{₹}x$.\n\nThe shopkeeper marks up the price by 50%. \nMarked Price (MP) = $\text{CP} + 50\%\text{ of CP} = x + 0.50x = 1.50x$.\n\nHe then offers a discount of 20% on the Marked Price. \nSelling Price (SP) = $\text{MP} - 20\%\text{ of MP} = \text{MP}(1 - 0.20) = \text{MP}(0.80)$.\n\nNow, substitute the expression for MP into the SP equation:\n$\text{SP} = (1.50x)(0.80) = 1.20x$.\n\nIt is given that the Selling Price (SP) is $\text{₹}1200$.\nSo, we can set up the equation:\n$1.20x = 1200$.\n\nTo find $x$ (the Cost Price):\n$x = \frac{1200}{1.20}$\n$x = \frac{1200}{\frac{120}{100}}$\n$x = \frac{1200 \times 100}{120}$\n$x = 10 \times 100$\n$x = 1000$.\n\nTherefore, the cost price of the article was $\text{₹}1000$.
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