The incident occurred near a rivulet of Oomari village, falling under the Highway police station, when they met a relative of theirs and stopped to drink water, police said.
The speeding vehicle crushed Praddyuman Singh and his father Kanhaiya Lal (40), and also hit his uncle Mukesh Kushwaha, an official said.
While the father-son duo died on the spot, Kushwaha suffered injuries and was later rushed to a hospital where he is undergoing treatment, police said.
Kushwaha said Praddyuman was returning home on motorcycle with his father after appearing in the board examination at Bhagwan Singh Inter College, Mudesi, when the accident took place.