Did they claim that they had managed to solve the problem?
=>Was the problem claimed that they had managed?
Do you think that they will have the chance to visit that place?
=>Are they thought to have the chance to visit that place?
Did they believe that the information was true?
=>Was the information believed was true?
Did anyone hope that there would be a significant change in the standards of living?
=>Was a significant change hoped in the standards of living?