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      Question

      Ratio between the age of Varsha, 8 years ago from now

      and age of Nidhi, 6 years hence from now, will be 9:16, respectively. Age of Priya, 3 years hence from now will be ____ more than age of Varsha, ___ years hence from now. Present age of Priya is 42 years and the present average age of Nidhi and Priya is ___ years. (Ages of all the given persons have integral value) The values given in which of the following options will fill the blanks in the same order in which it is given to make the statement true: I. 50%, 4, 34 II. 25%, 1, 42 III. 60%, 2, 31 
      A Only (I) Correct Answer Incorrect Answer
      B Only (II) and (III) Correct Answer Incorrect Answer
      C Only (III) and (I) Correct Answer Incorrect Answer
      D Only (I) and (II) Correct Answer Incorrect Answer
      E All (I), (II) and (III) Correct Answer Incorrect Answer

      Solution

      For I: Present age of Priya = 42 years
      Sum of present ages of Nidhi and Priya = 34 × 2 = 68 years
      Present age of Nidhi = 68 − 42 = 26 years
      Age of Nidhi 6 years hence from now = 26 + 6 = 32 years
      Age of Varsha 8 years ago from now = 32 × (9/16) = 18 years
      Present age of Varsha = 18 + 8 = 26 years
      Age of Priya 3 years hence from now = 42 + 3 = 45 years
      Age of Varsha 4 years hence from now = 26 + 4 = 30 years
      Required percentage = {(45 − 30)/30} × 100 = 50%

      Therefore, I is true. For II: Present age of Priya = 42 years
      Sum of present ages of Nidhi and Priya = 42 × 2 = 84 years
      Present age of Nidhi = 84 − 42 = 42 years
      Age of Nidhi 6 years hence from now = 42 + 6 = 48 years
      Age of Varsha 8 years ago from now = 48 × (9/16) = 27 years
      Present age of Varsha = 27 + 8 = 35 years
      Age of Priya 3 years hence from now = 42 + 3 = 45 years
      Age of Varsha 1 year hence from now = 35 + 1 = 36 years
      Required percentage = {(45 − 36)/36} × 100 = 25%

      Therefore, II is true. For III: Present age of Priya = 42 years
      Sum of present ages of Nidhi and Priya = 31 × 2 = 62 years
      Present age of Nidhi = 62 − 42 = 20 years
      Age of Nidhi 6 years hence from now = 20 + 6 = 26 years
      Age of Varsha 8 years ago from now = 26 × (9/16) = non-integer value.

      Therefore, III is false.
      Hence, option D (Only I and II).

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