While Sarah was allegedly murdered for unknown reasons by a Dutchman staying in the same houseboat, Alison walked out of her hotel in north Kashmir's Sonamarg Aug 17, 1981, never to return.
Investigations into the missing girl's disappearance went on for years. Nobody knew her whereabouts, and her parents continue to hope that she would return.
Her disappearance remains a mystery to this day.
The visually-impaired father of the Scottish girl, Kenny MacDonald, and her mother, Reta, visited Kashmir 17 times since her disappearance, hoping to find their daughter alive.
In 2011, her father told a Scottish newspaper: "I have just a wee bit of sight left - just a weak streak. I think it's been kept for Alison, to see her again. We will see her in this world again, of that we are sure, and it will be a great day."
The Ross-shire-based family, according to media reports, believed that Alison had joined nomadic tribes in the region, and could be found in Kashmir's inaccessible hills.
Newspapers in London continued to run headlines of Alison's disappearance long after local police declared that the young woman was "untraced" and the case was "closed".
A massive search operation was also started by the family in the Sonamarg area of the Valley, using low-flying helicopters. Hundreds of tribesmen and horses were roped into the effort to trace the British girl.
Till some years ago, the family would make a ritual visit to Hotel Glacier in Sonamarg every year. Alison had left her room from this hotel on that August morning of 1981.
While suspicion for Alison's disappearance swung from security men to wild animal attacks, some locals believe that the abominable Himalayan snowman, "Yeti", had made off with the girl.
People in Kashmir hope Sarah Groves's murder is solved quickly, and the murderer brought to justice.
"We are tourist-friendly, and cannot afford to have guests either disappearing under mysterious circumstances or murdered by fellow guests," said Abdul Rehman, 75, a houseboat owner here.
"We shall always remember her as a loving daughter. It is a state of mourning in our family," said Abdul Rahim Shoda, the owner of "New Beauty" houseboat where Sarah was found in a pool of blood with multiple stab wounds Saturday morning.