The question below is followed by two statements numbered I and II. Decide whether the data given in the statements are sufficient to answer the question.
What is Gita’s present age?
I. The present ages of Gita and her sister Hema are in the ratio 3 : 4, and Hema is 5 years older than Gita.
II. The sum of the present ages of Gita and Hema is 35 years.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Statement I alone is sufficient, but statement II alone is not sufficient.
A ratio gives the ages as \(3k\) and \(4k\); one more fact about the actual ages fixes \(k\).
Statement I alone:
Gita \(=3k\), Hema \(=4k\)
Hema \(-\) Gita \(=4k-3k=k=5\)
Gita \(=3\times5=\) 15 years: sufficient
Statement II alone:
Only the sum is known; for example 15 and 20, or 10 and 25, both give 35: not sufficient