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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. Aman and Bittu entered into a business partnership, contributing initially in the ratio 4:3. After one year, they infused additional capital in the ratio 3:1. Determine Aman’s initial investment. Statement I: Out of a total profit of Rs. 2,448, Aman’s share is Rs. 1,530. Statement II: Out of a total profit of Rs. 4,800, Bittu’s share is Rs. 1,800.
    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. Correct Answer Incorrect Answer
    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. Correct Answer Incorrect Answer
    C The data either in statement I alone or in statement II alone are sufficient to answer the question. Correct Answer Incorrect Answer
    D The data given in both statements I and II together are not sufficient to answer the question. Correct Answer Incorrect Answer
    E The data in both statements I and II together are necessary to answer the question. Correct Answer Incorrect Answer

    Solution

    ATQ, Let Aman and Bittu can be defined as A and B.

    So, A and B initially invest Rs. 4x and Rs. 3x, respectively. Let their additional investments be Rs. 3y for A and Rs. y for B. Then, the profit-sharing ratio becomes: A : B = (4x + 4x + 3y) : (3x + 3x + y) = (8x + 3y) : (6x + y) Statement I: As per the given information: (8x + 3y)/(14x + 4y) = 1530/2448 ⇒ (8x + 3y)/(14x + 4y) = 5/8 ⇒ Cross-multiplying: 64x + 24y = 70x + 20y ⇒ Simplifying: 6x = 4y ⇒ So, 3x = 2y Since we have two variables, the equation cannot be solved uniquely. Hence, Statement I alone is insufficient to determine the required values. Statement II: As per the question: (6x + y)/(14x + 4y) = 1800/4800 ⇒ (6x + y)/(14x + 4y) = 3/8 ⇒ Cross-multiplying: 48x + 8y = 42x + 12y ⇒ Simplifying: 6x = 4y ⇒ So, 3x = 2y Again, we have two unknowns, and the equation can't be solved. Therefore, Statement II alone is insufficient. Combining Statements I and II: Since both statements lead to the same equation (3x = 2y), we still cannot determine unique values for x and y. Therefore, the data in both Statements I and II together are not sufficient to answer the question.

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