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.

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