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      Question

      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 suicient to answer the question. X and Y started a business with investments of Rs. (x + 90) and Rs. (3x + 270), respectively. What is the investment of X? Statement I: The ratio of the annual profit share of X to Y is 1 : 3. Statement II: The difference between the profits earned by X and Y at the end of 8 months is Rs. 580.
      A The data given in both statements I and II together is not sufficient to answer the question. Correct Answer Incorrect Answer
      B The data in both statements I and II together is necessary to answer the question. Correct Answer Incorrect Answer
      C 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. Correct Answer Incorrect Answer
      D 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. Correct Answer Incorrect Answer
      E The data either in statement I alone or in statement II alone is sufficient to answer the question. Correct Answer Incorrect Answer

      Solution

      ATQ,

      Statement I: The annual profit-sharing ratio of Mini and Monu is: = (x + 90) : (3x + 270) = (x + 90) : [3(x + 90)] = 1 : 3 Since we cannot determine the exact value of 'x', statement I alone is not enough to answer the question. Statement II: The profit-sharing ratio of Mini and Monu after 8 months is: = (x + 90) × 8 : (3x + 270) × 8 = (x + 90) : (3x + 270) = (x + 90) : [3(x + 90)] = 1 : 3 Assume their profit shares are Rs. 'k' and Rs. '3k' respectively. Then, 3k - k = 580 So, 'k' = 290 Because (x + 90) can be any multiple of 290, the exact value of 'x' still cannot be found. Hence, statement II alone is also not sufficient. Conclusion: Even using both statements together, we cannot determine the value of 'x'. The data is not sufficient to answer the question.

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