Let's analyze the information given in each statement to see if we have enough to determine Ritika’s birth year.
Statement I: “Ritika at present is 25 years younger to her mother.”
This tells us that the age difference between Ritika and her mother is 25 years.
In equation form, if we let the mother’s birth year be M and Ritika’s birth year be R , then:
R = M + 25
However, without knowing the actual birth year of the mother (or any specific year), we cannot determine R uniquely.
Thus, Statement I by itself is not sufficient.
Statement II: “Ritika's sister who was born in 1964, is 35 years younger to her mother.”
This statement allows us to determine the mother’s birth year.
If the sister was born in 1964 and is 35 years younger than her mother, then their birth years differ by 35 years:
M = 1964 - 35 = 1929
Now we know the mother was born in 1929.
However, Statement II does not tell us anything about Ritika’s age or her relation to the mother.
Without knowing the 25-year difference between Ritika and her mother (as given in Statement I), we cannot find Ritika’s birth year based solely on Statement II.
Therefore, Statement II by itself is not sufficient.
Combine Statements I and II:
From Statement II, we already calculated the mother’s birth year as 1929.
Now, using Statement I, where Ritika is 25 years younger than her mother, we find:
R = 1929 + 25 = 1954
With both pieces of information, we can uniquely determine that Ritika was born in 1954.
Conclusion: Neither statement alone is sufficient, but when combined they provide enough information to answer the question.
The correct answer is: Option D – Both I and II are sufficient.