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11 January 2015, 10:10 | Updated: 11 January 2015, 10:14
The incident happened in Hayhill, Ayr, at around 3pm yesterday when the three men, claiming to be working in the local area, called at the 68-year-old woman's house.
They said they needed access to the premises for their work and once inside they distracted the woman and her 58-year-old brother, went upstairs alone and then left, police said.
Once they had left the house, the brother and sister realised that a five-figure sum of money was missing.
The three suspects are white, around 5ft to 6ft. One of the men had a heavy build, short dark brown hair and an Irish accent. He was wearing a dark jacket.
The other two police want to trace are of medium build and have short brown hair. One was wearing a blue jacket and the other a dark jacket.
Police have urged people to ask for identification if there are are any callers at their door, and recommended that elderly members of the community use a door chain to ensure callers cannot gain entry until they have shown identification.
Detective Sergeant Kevin Gilmour said: ''The householders are understandably distressed; these men duped them, rummaged through their home and stole from them.
''Extensive enquires are ongoing to find the men responsible who made off on foot from the house towards Mainholm Road.
''`I would urge anyone who saw them in the area, or think they know who they are to contact officers in Ayr via the non emergency number 101.
''I would also ask that if anyone else has been approached by these men or knows of someone who has, to call police.''