"Grandmother eats rice."
Translation:할머님께서 진지를 드세요.
It appears 진지 is an honorific noun used specifically with people of a grandparent's age. 식사 is for seniors, your boss, coworkers, etc. 밥 is for good friend that are your age and younger only.
Some nouns have honorific forms too. :)
The problem is that 진지 simply doesn't mean rice. It means a meal. 밥 on the other hand, actually means cooked rice, but can also mean food in general.
It looks like it means "meal". I'm not sure if this is an idiom or something, but perhaps it's more polite to refer to the meal as a whole than rice in particular?
'to eat', but honorific. Used when talking about people one deeply respects. Dictionary form: 드시다
진지 is meal or food, not rice. You would say someone is eating 진지 if you highly respect the person—the president eats 진지, older neighbour, teacher, grandparents, and so on.
My understanding is that ...드십니다 correct and ...드세요 is incorrect; ...드세요 indicates that grandmother is being offered rice to eat.