Question
The mixture contains Lemon and Mango juice in the ratio
of 9:5? Find the value of 'a' and 'p' Statement I: After removing 392 ml of the mixture, 'a' ml of Mango juice and 'a – 80' ml of Lemon are added to the remaining mixture, resulting in the final mixture having 50% Lemon. Statement II: After removing 280 ml of the mixture, 'a' ml of Mango juice is added to the mixture, and the final mixture has Mango juice amounting to 75% of the Lemon in the final mixture. 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 are 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 are not sufficient to answer the question. C) The data either in statement I alone or in statement II alone are sufficient to answer the question. D) The data given in both statements I and II together are not sufficient to answer the question. E) The data in both statements I and II together are necessary to answer the question.Solution
ATQ, Let quantity of Leomon and Mango juice in the original mixture is 9p ml and 5p ml respectively. Statement I: Quantity of Leomon in 392 ml of mixture = 9/14 × 392 = 252 ml Quantity of Mango juice in 392 ml of mixture = 392 – 252 = 140 ml According to question; 9p – 252 + a – 80 = 5p – 140 + a Or, 4p = 192 Or, p = 48 Quantity of original mixture = 48 × 14 = 672 ml So, data in statement I alone is sufficient to answer the question. Statement II: Quantity of Leomon in 280 ml of mixture = 9/14 × 280 = 180 ml Quantity of Mango juice in 280 ml of mixture = 280 – 180 = 100 ml According to question; (5p - 100 + a) = 0.75 × (9p - 180) Since, we cannot find the value of ‘a’ and ‘p’. So, data in statement II alone is not sufficient to answer the question.
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