Margaret went missing from her home in Godalming, Surrey, on Wednesday and police say she got on a train with a man who had bought tickets for Moreton-in-Marsh.
CCTV images show Margaret with a man on a train from Woking, in Surrey, to Basingstoke in Hampshire.
Margaret is described as white, with long blonde hair, blue eyes, 5 foot 5 tall and of a slim build. She was last seen wearing a navy blue hooded rain coat, dark bottoms and white trainers.
The male is described as in his early 20s.
He is around 6 foot, and of muscular build. He was wearing a burgundy long sleeve top, and black knee length shorts and carrying a back pack.
Anyone who sees Margaret, or has information that could help us trace her, is asked to call Surrey Police on 101 quoting 45170103539. Information can also be passed anonymously to the crimestoppers on 0800 555 111.