The question consists of two statements numbered “I

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.