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 Raman’s present age?
I. The present ages of Raman and his brother Vikas are in the ratio 5 : 7, and Vikas is 8 years older than Raman.
II. The sum of the present ages of Raman and Vikas is 48 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 \(5k\) and \(7k\); one more fact about the actual ages fixes \(k\).
Statement I alone:
Raman \(=5k\), Vikas \(=7k\)
Vikas \(-\) Raman \(=7k-5k=2k=8\), so \(k=4\)
Raman \(=5\times4=\) 20 years: sufficient
Statement II alone:
Only the sum is known; for example 20 and 28, or 18 and 30, both give 48: not sufficient