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Question
A shopkeeper carns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is
45:56
45:51
47:56
47:51
ANSWER : 1
Descrption
<p style="margin-left:0px;">CP = Cost Price of the book MP = Marked (Printed) Price of the book SP = Selling Price of the book D = Discount Percentage P = Profit Percentage</p><p style="margin-left:0px;">We are given:</p><ol><li>Profit Percentage (P) = 12%</li><li>Discount Percentage (D) = 10%</li></ol><p style="margin-left:0px;">We need to find the ratio of CP to MP.</p><p style="margin-left:0px;">We know that:</p><p style="margin-left:0px;">Profit Percentage (P) = [(SP - CP) / CP] * 100 Discount Percentage (D) = [(MP - SP) / MP] * 100</p><p style="margin-left:0px;">Let's use these formulas to find CP/MP:</p><ol><li>Profit Percentage (P) = 12% = 12/100 = 0.12</li><li>Discount Percentage (D) = 10% = 10/100 = 0.10</li></ol><p style="margin-left:0px;">Using the profit formula:</p><p style="margin-left:0px;">0.12 = [(SP - CP) / CP]</p><p style="margin-left:0px;">Now, let's use the discount formula:</p><p style="margin-left:0px;">0.10 = [(MP - SP) / MP]</p><p style="margin-left:0px;">We can rearrange the first equation to find SP in terms of CP:</p><p style="margin-left:0px;">SP = CP + 0.12 * CP SP = 1.12 * CP</p><p style="margin-left:0px;">Similarly, we can rearrange the second equation to find SP in terms of MP:</p><p style="margin-left:0px;">SP = MP - 0.10 * MP SP = 0.90 * MP</p><p style="margin-left:0px;">Now, we can set these two expressions for SP equal to each other since they both represent the selling price:</p><p style="margin-left:0px;">1.12 * CP = 0.90 * MP</p><p style="margin-left:0px;">Now, let's find the ratio of CP to MP:</p><p style="margin-left:0px;">CP/MP = 0.90 / 1.12</p><p style="margin-left:0px;">To simplify this ratio, we can multiply both the numerator and denominator by 100 to get rid of the decimals:</p><p style="margin-left:0px;">CP/MP = (0.90 * 100) / (1.12 * 100) CP/MP = 90/112</p><p style="margin-left:0px;">Now, we can simplify this ratio by dividing both the numerator and denominator by their greatest common divisor, which is 2:</p><p style="margin-left:0px;">CP/MP = (90/2) / (112/2) CP/MP = 45/56</p><p style="margin-left:0px;">So, the ratio of the cost price (CP) to the marked price (MP) of the book is 45:56. The correct answer is 45:56.</p>
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