Question
The sugar bag's cost price and marked price have a ratio
of 4:7. If the bag is sold for Rs.600, calculate the profit %. Statement I: The profit % and the discount % allowed on the sugar bag's sale are in the ratio 7:8, respectively. Statement II: The profit earned from selling the sugar bag is half of the discount allowed on its sale. The question consists of two statements numbered "I and II" given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. A) The data in statement I alone are sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. B) The data in statement II alone are sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. C) The data either in statement I alone or in statement II alone is sufficient to answer the question. D) The data given in both statements I and II together is not sufficient to answer the question. E) The data in both statements I and II together is necessary to answer the question.Solution
ATQ, Let the marked price and cost price of the Sugar bag be Rs. '7x' and Rs. '4x', respectively. Statement I: Let the profit % earned and discount % allowed on selling the Sugar bag be 7y% and 8y% respectively. According to the statement: 4x × {(7y + 100) /100} = 600 ...... (I) And 7x × {(100 - 8y) /100} = 600 ....... (II) On comparing equation (I) and (II) , we have; 4x × {(7y + 100) /100} = 7x × {(100 - 8y) /100} Or, 28y + 400 = 700 - 56y Or, 84y = 300 So, y = (25/7) So, profit % = 7 × (25/7) = 25% So, data in statement I alone is sufficient to answer the question. Statement II: According to the statement: (7x - 600) = 2 × (600 - 4x) Or, 7x - 600 = 1200 - 8x Or, 15x = 1800 So x = 120 So, cost price of the article = 120 × 4 = Rs. 480 So, profit earned = 600 - 480 = Rs. 120 So, profit % = (120/480) × 100 = 25% So, data in statement II alone is sufficient to answer the question
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