In Darbhanga, a new battery-acid rickshaw, like the one Rai drives, sells for about 175,000 rupees, or $2,100. That’s half the price of a new natural gas-powered rickshaw. Charging the battery costs 20 rupees (25 cents), a quarter of the price of filling a tank of gasoline.

The discounts seem to be working. Reliance Industries, India’s largest company, is converting its three-wheeled cargo vehicles from petrol to electric. Food delivery services are going electric as quickly as possible.

Chetan Maini, whose company Sun Mobility builds charging infrastructure, said the business was growing rapidly. Battery prices are falling, helping to reduce the cost of electric two- and three-wheeled vehicles. “When the crossover point occurs here,” Mr. Maini predicted, “the effect is very fast, in a hockey stick fashion, because it is more sensitive to price.”

About 200 electric rickshaws are sold in Darbhanga a month, according to Balaji Motors, a dealer. In two years, one sales manager estimates, electric rickshaws will dominate the streets.

By Indian standards, Darbhanga, with a population of 300,000, could be considered a sleepy town. Quiet, however, it is not. Loudspeakers play music in the temples and advertising jingles in the open-air shops. The horns honk; the engines sputter.

In that soundscape, Mr. Rai’s purring electric rickshaw is a relative rarity, one that delighted a recent passenger, a retired teacher named Satyen Vir Jha.