NHK quoted police in Miyagi prefecture as saying the two were weak but conscious.
An NHK reporter, quoting a doctor at the hospital to which the two were taken by helicopter, said the two had been trapped in their kitchen after the massive earthquake and survived by eating yoghurt and other food in the refrigerator.
The grandson eventually made it to the roof and waved down a rescue helicopter, the NHK reporter said.
The youth, Jin Abe, had low body temperature, was shaking and had no feeling in his left ankle, the reporter said.
An official at Ishinomaki’s Red Cross hospital said the two had been carried into the hospital and were getting treatment.
“I only had a glimpse of the elderly woman, who had her eyes closed,” the official said. “She didn’t appear to be dead,” the official said when asked if she was conscious.
Ishinomaki police were not immediately available to confirm the report.
On Saturday, Kyodo news agency and the military reported the “miracle rescue” of a young man pulled from the rubble of his home, only to find out that he had been in an evacuation center beforehand and just returned to his home.
