Jim and Freda tell lies on Saturdays and Sundays. Freda also tells lies on Tuesdays, Wednesdays and Thursdays. They tell the truth on the days they are not lying. If they both claim to have lied yesterday then what day is it today?
Let's go through the days: Monday: they both tell the truth on Mondays, and they both lie at weekends, so Monday fits; Tuesday: Jim would be lying on a day he tells the truth, because on Monday and Tuesday he tells the truth, so Tuesday can be eliminated; Wednesday: Freda lies on Wednesdays and Tuesdays, so if she says she was lying on Tuesday she would be telling the truth, so Wednesday can be eliminated; Thursday: can be eliminated, for the same reason as Tuesday; Friday: Jim tells the truth on weekdays so could not have been lying on Thursday, so Friday can be eliminated; Saturday: both lie on Saturdays and tell the truth on Fridays, so by lying about lying on Friday, they imply that they were telling the truth on Friday, so Friday fits; Sunday: can be eliminated because they would be telling the truth about lying on Saturday. There seem to be two answers: Monday and Friday.