Rescue workers retrieved several people left trapped under tonnes of debris after the building collapsed in a crowded neighbourhood of Indore on Saturday night.
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"We pulled out 12 people from under the debris. Ten of them have died," police inspector Sanju Kamle told AFP.
Local media reports said the collapse took place after a car drove into the building's front portion.
"We are investigating. At the moment it is difficult to say how it collapsed," Kamle said.
Rescue workers had managed to clear the debris and some of the injured were being treated at a government-run hospital, Kamle added.
Building disasters are common in Indian cities where millions are forced to live in cramped, run-down properties due to spiralling real estate prices and a lack of proper housing.
Activists say owners often cut corners on construction to save costs with little regard to safety.
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Some 30 people perished in September last year when a 117-year-old apartment building collapsed in India's financial hub of Mumbai.
And in 2013, 60 people were killed when a residential block came crashing down in one of the country's worst housing disasters.
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