Explanation:

Let's denote 'older than' with '>' and 'younger than' with '<'. 1. Amit is older than Vijay: $A > V$ 2. Shaun is older than Joy: $S > J$ 3. Ketan is younger than Joy: $K < J$, which means $J > K$ 4. Vijay is older than Shaun: $V > S$ \nNow, let's combine these relationships to form a single chain of age order from oldest to youngest: \nFrom (4), we have $V > S$.\nFrom (2), we have $S > J$.\nFrom (3), we have $J > K$. \nCombining these three, we get the sequence: $V > S > J > K$. \nNow, incorporate statement (1): $A > V$.\nSo, the complete sequence from oldest to youngest is: $A > V > S > J > K$. \nFrom this chain, it is clear that Ketan is the youngest person in the group. \nAnalyzing the options: (1) Shaun: This is incorrect. Shaun is older than Joy and Ketan ($S > J > K$). (2) Ketan: This is correct. Ketan is the youngest in the derived sequence $A > V > S > J > K$. (3) Joy: This is incorrect. Joy is older than Ketan ($J > K$). (4) Vijay: This is incorrect. Vijay is older than Shaun, Joy, and Ketan ($V > S > J > K$). \nThe logically derived answer is Ketan. Please note that the provided answer key in the document indicates option (1) Shaun as correct, which contradicts this derivation. Shaun is older than Joy and Ketan, so he cannot be the youngest.