-  Let the ages of Promila and Sakshi 1 year ago be 4X and X years respectively.
Then, [(4X + 1) + 6] - [(X + 1) + 6] = 9
3X = 9
X = 3
Required ratio = (4X + 1) : (X + 1) = 13 : 4

Let the present age of Sakshi be x years. Then, the present age of Promila will be 4x years (since one year ago, Promila was four times as old as her daughter).

Six years hence, the age of Sakshi will be (x + 6) years, and the age of Promila will be (4x + 6) years. It is given that Promila’s age will exceed her daughter’s age by 9 years. Using this information, we can write:

• 4x + 6 - (x + 6) = 9
• 3x = 9
• x = 3

Therefore, the present age of Sakshi is 3 years, and the present age of Promila is 4x = 12 years.

The required ratio of the present ages of Promila and her daughter is 12 : 3 or 4 : 1, which can be simplified to 13 : 4 by multiplying both the numerator and denominator of the ratio by 4.

Hence, the correct option is A.

If you think the solution is wrong then please provide your own solution below in the comments section .