Data Sufficiency: Mohita vs Shubham Age

The question asks to determine if Mohita is younger or older than Shubham.

Statement 1 Analysis

Statement 1 says Mohita is exactly 35 years younger than her father.

• Let M be Mohita's current age.
• Let $F_M$ be her father's current age.
• The relationship is $M = F_M - 35$.
• This statement provides no information about Shubham or Mohita's absolute age.
• Therefore, Statement 1 alone is not sufficient.

Statement 2 Analysis

Statement 2 says Shubham was born in 1954 and is exactly 34 years younger than his father.

• Let S be Shubham's current age.
• Let $F_S$ be his father's current age.
• Shubham's birth year is 1954.
• The relationship is $S = F_S - 34$.
• We can determine Shubham's age in any given year, but this statement provides no information about Mohita.
• Therefore, Statement 2 alone is not sufficient.

Combined Statements Analysis

To compare Mohita's and Shubham's ages, we need information linking them. The problem implies they are siblings and likely share the same father.

• Assume Mohita's father and Shubham's father are the same person. Let F be the father's age.
• From Statement 1: $M = F - 35$.
• From Statement 2: Shubham born in 1954, and $S = F - 34$.
• Comparing the two equations: $S = F - 34$ and $M = F - 35$.
• This means $S = M + 1$. Shubham is 1 year older than Mohita.
• For example, in the year 2023:
• Shubham's age $S = 2023 - 1954 = 69$.
• Father's age $F = S + 34 = 69 + 34 = 103$.
• Mohita's age $M = F - 35 = 103 - 35 = 68$.
• Thus, Shubham (69) is older than Mohita (68).
• Both statements are necessary to establish the relationship between Mohita's and Shubham's ages.

Conclusion

Since neither statement alone is sufficient, but both statements together are necessary to answer the question, the correct option is B.