They had cooked up the story to flee their homes in search of "money" in any big city to help their parents, SHO at the Kahnuwan Police Station in Gurdaspur, Harjit Singh said.
The girls returned to Amritsar and from there the police brought them to their home in Gurdaspur, he said, adding "they will be counselled and no case will be registered against them."
Seventeen-year-old Sophia had earlier said that her sister Lovepreet Kaur (19) and her cousin Nisha (18) had drowned in a canal while taking a selfie, but later spilled the beans, the SHO said.
"They took a lift from a truck driver telling him that they had just joined the police department and were going to join work at Chandigarh," Singh said.
Later, at Delhi when they realised their mistake and ran out of money, they decided to return home, the SHO said.