A Ford Motor Co. investment arm is among the companies pouring $24 million into a vehicle-rental startup in India, the latest development in the race to use technology in new ways to target consumers in the world’s second-most-populous country.

Bangalore-based Zoomcar allows users to rent its vehicles for as little as an hour at a time, a model similar to the U.S.’s Zipcar Inc., which Avis Budget Group acquired for about $500 million in 2013.

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