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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. There are four friends P, Q, R and S. Find the age of S? Statement-I: The ratio of present ages of P to Q, Q to R, R to S and S to P is (x - 6): (x - 14), (x - 14): (x + 2), (x + 2): (x + 10) and 5:3 respectively. Statement-II: The ratio of present ages of P to Q, Q to R, R to S is (x - 6): (x - 14), (x - 14): (x + 2) and (x + 2): (x + 10) respectively, and average present ages of four friends is 28 years.
      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: (Ratio of Age of P and Q) × (Ratio of Age of Q and R) × (Ratio of Age of R and S) = Ratio of Age of P and S (x - 6)/(x - 14) × (x - 14)/(x + 2) × (x + 2)/(x + 10) = 3/5 (x – 6)/(x + 10) = 3/5 5x – 30 = 3x + 30 5x – 3x = 30 + 30 2x = 60 x = 30 Ratios of the ages of P, Q, R and S are known, but the exact age of S can’t be determined. So, statement-I alone is not sufficient to answer the question. Statement-II: The ratio of present ages of P to Q, Q to R, R to S is (x - 6): (x - 14), (x - 14): (x + 2) and (x + 2): (x + 10) respectively. So, ratio of ages: P: Q: R: S = (x - 6): (x - 14): (x + 2): (x + 10) Let, k is some constant. So, ages of P, Q, R and S be (x – 6) × k, (x – 14) × k, (x + 2) × k, (x + 10) × k According to question, (x – 6) × k + (x – 14) × k + (x + 2) × k + (x + 10) × k = 28 × 4 Since, there are two variables but one equation. So, statement-II alone is not sufficient to answer the question. Combining Statement-I and Statement-II, we get, (Ratio of Age of P and Q) × (Ratio of Age of Q and R) × (Ratio of Age of R and S) = Ratio of Age of P and S (x - 6)/(x - 14) × (x - 14)/(x + 2) × (x + 2)/(x + 10) = 3/5 (x – 6)/(x + 10) = 3/5 5x – 30 = 3x + 30 5x – 3x = 30 + 30 2x = 60 x = 30 So, 24k + 16k + 32k + 40k = 112 112k = 112 k = 112/112 = 1 Therefore, age of S = 40 years So, data in statements I and II together are necessary to answer the question.

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