RANWAN, India — In this north Indian village, workers recently dismantled stacks of burned and mildewed rice while flies swarmed nearby over spoiled wheat. Local residents said the rice crop had been sitting along the side of a highway for several years and was now being sent to a distillery to be turned into liquor.

Just 180 miles to the south, in a slum on the outskirts of New Delhi, Leela Devi struggled to feed her family of four on meager portions of flatbread and potatoes, which she said were all she could afford on her disability pension and the irregular wages of her day-laborer husband. Her family is among the estimated 250 million Indians who do not get enough to eat.

Such is the paradox of plenty in India’s food system. Spurred by agricultural innovation and generous farm subsidies, India now grows so much food that it has a bigger grain stockpile than any country except China, and it exports some of it to countries like Saudi Arabia and Australia. Yet one-fifth of its people are malnourished — double the rate of other developing countries like Vietnam and China — because of pervasive corruption, mismanagement and waste in the programs that are supposed to distribute food to the poor.

“The reason we are facing this problem is our refusal to distribute the grain that we buy from farmers to the people who need it,” said Biraj Patnaik, who advises India’s Supreme Court on food issues. “The only place that this grain deserves to be is in the stomachs of the people who are hungry.”