The following questions are accompanied by three statements (I), (II), and (III). You have to determine which statements(s) is/are sufficient/necessary to answer the questions. What is the present age of Priyanka? Statement I: When Himani was 10 years old, Priyanka’s age was half than Himani’s age Statement II: Four years ago, Sakshi’s age was three times than Priyanka’s age. Statement III: At present, Sakshi’s age is double than Himani’s age. Correct Answer All I, II and III together From Statement I, When Himani was 10 years old, Priyanka’s age was half than Himani’s age It means that Priyanka is 5 years younger than Himani Hence, this statement is not enough to get the answer From Statement III, At present, Sakshi’s age is double than Himani’s age Let the current age of Himani be x years Then, the current age of Sakshi will be 2x years But, this statement alone is not enough to get the answer From Statement II, Four years ago, Sakshi’s age was three times than Priyanka’s age Current age of Sakshi is 2x years Then, four years ago her age was 2x - 4 years Four years ago Priyanka’s age will be (2x - 4)/3 years This statement alone is also not enough to get the answer Considering I, II and III together, From II, the current age of Himani is x years From III, four years ago Priyanka’s age was (2x - 4)/3 years ----(1) Four years ago Himani age will be x - 4 years From I, Four years ago Priyanka’s age will be = x - 4 - 5 years = x - 9 years ----(2) From (1) and (2), (2x - 4)/3 = x - 9 ⇒ 2x - 4 = 3x - 27 ⇒ 27 - 4 = 3x - 2x ⇒ x = 23