Answer: Option A
:
A
Let us assume that Amita is lying and Sunita and Vinita are telling the truth
Then Sunita is not the youngest $=>$ from Vinita's $2^{nd}$ statement, Vinita is not the eldest.
Since Amita is lying, so from her $3^{rd}$ statement, Amita is not the eldest.
Now, since Sunita is not the youngest and Vinita is elder to Sunita $=>$ Sunita is not the eldest.
Also, since, Amita is not the eldest $=>$ Vinita has to be the eldest.
But, from her $2^{nd}$ statement, Vinita is not the eldest; so, our assumption is incorrect
as per our assumption Sunita isn't lying which means our assumption is incorrect.
Let us assume that Sunita is lying and Amita and Vinita are telling the truths.
Then, from Amita's $1^{st}$ statement, Sunita is the youngest. Since, Sunita is lying so, from Sunita's $2^{nd}$ statement, Vinita is not elder to her, so this means that Vinita is either of the same age as her or younger than her. From Vinita's $1^{st}$ statement, Sunita cannot be of the same age as Vinita $=>$ Sunita should be elder than Vinita but also Sunita is the youngest $=>$ contradiction $=>$ our assumption is incorrect $=>$ Sunita isn't lying.
Since, neither Amita nor Sunita is lying $=>$ Vinita must be lying.
Vinita is lying and Sunita and Amita are telling the truths.
Sunita is the youngest and all are above 24 years of age and Vinita is elder to Sunita. So, the least possible age for Sunita is 25 years and Amita and Vinita are more than 25 years of age $=>$ as per Sunita's $1^{st}$ statement, Vinita is 26 years old.
Since, Vinita is lying and Sunita is the youngest, so from her $2^{nd}$ statement, Vinita is not the eldest $=>$ Amita is the eldest. Since, Vinita is 26 years of age and Vinita is elder to Sunita and the least possible age for Sunita is 25 years $=>$ Sunita is 25 years of age.
Amita is the eldest.