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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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