Concept:To find Guna's age, we need a direct or indirect relation connecting Guna to the given ages.
Explanation:Statement I says Guna, Vinay and Keshav are of the same age.
So,
Guna=Vinay=Keshav.
But this alone does not give any numerical value.
Therefore, Statement I alone is not sufficient.
Statement II says:
Vinay+Keshav+Arjun=32Also,
Arjun=Vinay+Keshav.
Substituting this into the sum:
(Vinay+Keshav)+(Vinay+Keshav)=322(Vinay+Keshav)=32Vinay+Keshav=16So,
Arjun=16 years.
But Guna is not mentioned anywhere in Statement II.
Hence, Statement II alone is also not sufficient.
Combining both statements:
From I:
Guna=Vinay=KeshavFrom II:
Vinay+Keshav=16Since
Vinay=Keshav, we get:
2×Vinay=16Vinay=8 years
Therefore,
Guna=8 years.
So both statements together are needed to answer the question.
Answer:Both statements together are Needed.