Suman's statement ' I am the eldest if and only if Renu is not the youngest' implies that either Suman is the eldest, Renu midway and Jyoti the youngest or Jyoti is the eldest, Suman the next and Renu the youngest. In either of the cases we see that Renu is younger to Suman and this agrees with Renu's statement 'Suman is elder to me.' Thus both Suman and Renu are speaking the truth and Jyoti is telling a lie. As Jyoti's statements 'I am the eldest’ and 'Renu is the youngest' cannot be correct, the second alternative of Suman's statement, i.e. Suman is the eldest, Renu the next and Jyoti the youngest, must hold.
Suman is elder to Renu by three years; combining this with Suman's last statement, we find that Renu is a year older than Jyoti. Let us next consider the three parts of Renu's first statement, one at a time. Renu cannot be 24 years old as according to Renu, Suman is not 27. Jyoti cannot be 25 years because if that were so, Jyoti's statement 'all are above 24 years' would hold and we know that Jyoti is lying. That leaves us with the last alternative i.e. Suman is 26, which places Renu at 23 and Jyoti at 22.