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

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).