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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 sufficient to answer the question. P, Q and R entered into a business with certain amount of initial investments. After one year, they made additional investments of certain amount. If total profit earned at the end of 2 years is Rs. 8640, then find the profit share of Q. Statement I: Initial investment made by P, Q and R is Rs. 960, Rs. 1200 and Rs. 1440 respectively and after one year they made additional investment in the ratio of 31:35:39 respectively. Statement II: Initial investment made by P, Q and R are in the ratio of 4:5:6 respectively and after 1 year they made additional investment of Rs. (x + 180), Rs. (x + 260) and Rs. (x + 340) respectively.
      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

      Statement I: Let additional investment made by P, Q and R be Rs. 31a, Rs. 35a and Rs. 39a respectively. Ratio of profit share of P, Q and R = [960 × 2 + 31a]:[1200 × 2 + 35a]:[1440 × 2 + 39a] = (1920 + 31a):(2400 + 35a):(2880 + 39a) Profit share of Q = (2400 + 35a)/(7200 + 105a) × 8640 So, data in statement I alone is not sufficient to answer the question. Statement II: Let initial investment made by P, Q and R is Rs. 4y, Rs. 5y and Rs. 6y respectively. Ratio of profit share of P, Q and R = [4y × 2 + x + 180]:[5y × 2 + x + 260]:[6y × 2 + x + 340] = (x + 8y + 180):(x + 10y + 260):(x + 12y + 340) Profit share of Q = (x + 10y + 260)/(3x + 30y + 780) × 8640 So, data in statement II alone is not sufficient to answer the question. Combining statement I and II: (x + 180)/(x + 260) = 31/35 35x + 6300 = 31x + 8060 4x = 1760 x = 440 Ratio of profit share of P, Q and R = [960 × 2 + 620]:[1200 × 2 + 700]:[1440 × 2 + 780] = 2540:3100:3660 = 127:155:183 So the profit share of Q = 155/(127 + 155 + 183) × 8640 = Rs. 2880 So data in statements I and II together are necessary to answer the question.

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