The driver of the allegedly overloaded car lost control of it when he was attempting to avoid a crash with another vehicle, local media reported.
The group of 16 pilgrims from Batala tehsil in Gurdaspur district of Punjab have come to praise at the Dera Vadbhag Singh Gurdwara, near Una, and the accident has taken place while they were returning, the police said.
In a separate incident, 15 people were injured when a car went off the road in Mandi district of Himachal Pradesh.
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All victims have reportedly come to the area for pilgrimage and religious ceremonies.
Deputy Superintendent of Police (DSP) Chandrapal Singh said the injured persons' conditions don't raise concerns.