The truck flipped over at a curve in the road in Himachal Pradesh state’s Chamba district on Wednesday night, said police Officer Madhusudan, who uses only one name.
Rescuers recovered 33 bodies and took seven injured people to a hospital, he said.
The Press Trust of India news agency said the gorge was 300 feet deep. The region is nearly 100 miles northwest of the town of Dharmsala.
Another seven people were killed in the other nearby accident when their bus plunged into a gorge, Officer Madhusudan said. They were being driven home from a nearby power project.
The drivers in both accidents were killed, and police were investigating what caused the crashes, Officer Madhusudan said.
India, the world’s second most populous nation, has the highest annual road death toll, according to the World Health Organization. More than 110,000 people die each year across the country in crashes caused by speeding, bad roads, overcrowding and poor vehicle maintenance, according to police.