The city-contracted company whose school bus fatally struck a 10-year-old girl in Brooklyn last week was granted a massive pay increase without adequate evaluation of its safety record, City Comptroller Scott Stringer charges.

The DOE’s “deeply opaque procurement policies” are taking NYC taxpayers for a ride — and putting kids in possible danger, Stringer said in a blistering letter sent Friday to schools Chancellor Richard Carranza.

Quality Transportation — or QTC, which operated the bus that killed fourth-grader Patience Albert — was awarded a DOE contract “extension” that calls for a more-than 11-fold increase in payment. It rose from an original $22.9 million for one year in 2014 to $270.3 million for nine years though June 2023 — adding about $7 million a year to the price, Stringer found.

The lucrative deal is one of 69 extensions approved last year by the DOE totaling $9.1 billion for 28 school bus companies, the comptroller tallied.

Stringer rejected them all in December, and sent them back to the DOE to explain the skyrocketing costs and why the contracts were not competitively bid, records show.

The comptroller has previously demanded information on how the DOE evaluates the bus companies’ past performance, including integrity and safety.

The DOE has yet to respond, he said.

“Sadly, this lack of concern over proper contracting not only undercuts the city’s commitment to sound fiscal control, but also adds unnecessarily to the risks that can affect the safety and health of our school children,” Stringer told Carranza.

The Post reported last June that the DOE had awarded a series of “emergency” bus-service extensions costing taxpayer millions of dollars in exorbitant costs.

One DOE insider called it the “school-bus gravy train.”

Stringer said his concerns took on urgency after the Feb. 25 death of 10-year-old Patience Albert in East New York. The student at Achievement First Linden Elementary School was mowed down by the yellow bus in a crosswalk at Crescent Street and Wortman Avenue. Her 15-year-old brother, Merzae, walking with her, suffered a leg injury. The bus had no passengers.

The driver, Pedro Colon, 61, was turning right onto Wortman Avenue from Crescent Street when he struck Patience, police said. He was charged with failure to yield to a pedestrian and failure to exercise due care.

The DOE said Colon, who was suspended, had no disciplinary history.

Whistleblowers say the DOE’s Office of Pupil Transportation is cozy with the bus companies, and goes too easy on removing bus drivers and attendants for misconduct.

Quality Transportation operates 234 bus routes for the DOE, officials said. Between January and June 2019, the company received four safety-related complaints from 52,000 rides. The OPT found misconduct in each case, and slapped the company with warnings. A spokeswoman said two offenses involved driving, but she would not elaborate.

The “core problem” with DOE, Stringer wrote, is that, “Unlike every mayoral agency in the city, the DOE does not use standardized performance evaluations with established metrics to assess how well a vendor is meeting its obligations. This is true for all contracts at DOE not just those pertaining to buses.

“The DOE often uses the same contractors over and over again, such as QTC, without properly evaluating their performance or ensuring that taxpayers are getting the service they paid for.”

DOE officials did not respond to Stringer’s letter, saying it was under review.