Question

The following question is accompanied by three statements (A), (B) and (C). You have to determine which statement(s) is/are sufficient/necessary to answer the question.
What is the ratio of the present ages of X and Y?
A. The ratio between the present ages of X and Y after 10 years is 11:15.
B. The present age of Y is $66\frac{2}{3}\%$ more than that of X.
C. The product of the present ages of X and Y is 240 years.

• A. Any of them
• B. Only C and either A or B
• C. Any two of them
• D. Only A and B together

Answer 1

Answer: (D)

Only A and B together

Answer 2

Let's analyze the statements:
Statement A: The ratio of X and Y's ages after 10 years is 11:15, providing future age information but not current ages.
Statement B: Y's present age is $66\frac{2}{3}\%$ more than X's, indicating a relationship but not exact ages.
Statement C: The product of their ages is 240 years, giving a product but no individual ages.
Combinations:
1. Any single statement : None provides sufficient information for the age ratio.
2. C and A or B : Still lacks enough info for individual ages or the ratio.
3. Any two statements : No combination gives sufficient data to find the exact ratio.
4. A and B together : Provides the necessary relationship to determine their current ages and ratio.
So, the correct option is (D) : Only A and B together are sufficient to find the ratio of X and Y's present ages.