Explanation:

Let's establish the age relationships: 1. Amit > Vijay 2. Shaun > Joy 3. Joy > Ketan 4. Vijay > Shaun \nCombining these statements:\nFrom (3), we have $\text{Joy} > \text{Ketan}$.\nFrom (2), we have $\text{Shaun} > \text{Joy}$. So, $\text{Shaun} > \text{Joy} > \text{Ketan}$.\nFrom (4), we have $\text{Vijay} > \text{Shaun}$. So, $\text{Vijay} > \text{Shaun} > \text{Joy} > \text{Ketan}$.\nFrom (1), we have $\text{Amit} > \text{Vijay}$. So, $\text{Amit} > \text{Vijay} > \text{Shaun} > \text{Joy} > \text{Ketan}$. \nThe complete order from oldest to youngest is Amit, Vijay, Shaun, Joy, Ketan. \nOption (A) Shaun: Shaun is older than Joy and Ketan, so not the youngest.\nOption (B) Ketan: Ketan is younger than Joy, who is younger than Shaun, who is younger than Vijay, who is younger than Amit. Thus, Ketan is the youngest. This is the correct option.\nOption (C) Joy: Joy is older than Ketan, so not the youngest.\nOption (D) Vijay: Vijay is older than Shaun, Joy, and Ketan, so not the youngest.