Step 1: Understanding the Question:
We need to determine the age order of four sisters based on a set of logical statements to find the youngest one.
Step 3: Detailed Explanation:
Let's analyze the statements step-by-step to rank them from oldest (1st) to youngest (4th):
• Statement (i): "Sita is the oldest."
This places Sita firmly in the 1st position.
• Statement (ii): "Latha is not the oldest."
Since we already know Sita is the oldest, this statement is consistent but doesn't immediately give a new position for Latha.
• Statement (iii): "Gita is younger to Rita."
This means Rita is older than Gita. Since Sita is 1st, Rita and Gita must occupy some combination of 2nd, 3rd, or 4th places, with Rita always ahead of Gita.
• Statement (iv): "Gita is not the youngest."
This means Gita cannot be in the 4th position.
Now let's synthesize:
Sita is 1st.
Gita must be younger than Rita, so Gita cannot be 2nd (because then Rita would have to be 1st, which is taken by Sita).
Therefore, Rita must be 2nd and Gita must be 3rd.
The only remaining position is the 4th (youngest) position, and the only sister left to place is Latha.
So the final order from oldest to youngest is: Sita, Rita, Gita, Latha.
Thus, Latha is the youngest.
Step 4: Final Answer:
Latha is the youngest sister.