An Unsuitable Job for a Woman - P. D. James

Meet Cordelia Gray: twenty-two, tough, intelligent and now sole inheritor of the Pryde Detective Agency. Her first assignment finds her hired by Sir Ronald Callender to investigate the death of his son Mark, a young Cambridge student found hanged in mysterious circumstances. Required to delve into the hidden secrets of the Callender family, Cordelia soon realises it is not a case of suicide, and that the truth is entirely more sinister.