The following is a conversation between Poornima and Riya.
Poornima: I'm not over 30 and that's for sure.
Riya: I am 28 and you are undoubtedly at least 5 years older to me.
Poornima: You got it all wrong; you are at least 29.
You know that both of the women are lying about their ages in all the three statements. Can you calculate their real ages?
Solution:
Since both of them lied in all three statements, this means that the opposite is true. So the changed statements will be:
Poornima: I am surely over 30.
Riya: I am not 28 and you are at most 4 years older to me.
Poornima: You are at most 28.
Poornima is 31 years old at least as can be concluded from the first statement. Combining the second and the third statement, we can accomplish that Riya is at most 28 years old. Hence, the possible ages of Poornima and Riya can be:
Poornima: 31, 32, 33, 34, 35, 36...
Riya: 22, 23, 24, 25, 26, 27...
Now, reading the second statement again, we can conclude that the difference between the ages of Poornima and Riya is at max 4 years.
This brings us the result that Poornima is 31 years old whereas Riya is 27 years old.