Question

The Given question is followed by two statements A and B. You are to determine whether the data given in the statements is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose between the possible answers.
The ages of Shruti and Aditi are in the ratio of 14:11. What is the age of Shruti?
A After 6 years the ratio of Shruti's and Aditi's ages will be 17:14.
B. The ages of Aditi and Tulika are in the ratio of 11:6.

• A. The statement A alone is sufficient to answer the question, but the statement B alone is not sufficient.
• B. The statement B alone is sufficient to answer the question, but the statement A alone is not sufficient.
• C. Both statements A and B together are needed to answer the question.
• D. Either the statement A alone or statement B alone is sufficient to answer the question.
• E. Cannot get the answer from the statement A and B together, but need even more data.

Answer 1

The Correct Option is A

We can solve this problem using only statement A.
Let Shruti's current age be 14x and Aditi's current age be 11x.
After 6 years:

• Shruti's age will be 14x + 6
• Aditi's age will be 11x + 6

According to statement A, the ratio of their ages after 6 years will be 17:14
So, \(\frac{(14x + 6) }{ (11x + 6) }= \frac{17 }{ 14}\)
Cross-multiplying, we get:
14(14x + 6) = 17(11x + 6)
196x + 84 = 187x + 102
9x = 18
x = 2
Therefore, Shruti's current age is 14x = 14 \(\times\) 2 = 28
Final Answer: The statement A alone is sufficient to answer the question, but the statement B alone is not sufficient.
So the correct option is (A)