You have $99$ bags, each containing various numbers of apples and oranges. Prove that there exist $50$ bags among these which together contain at least half the apples and at least half the oranges.
Needless to say, you may not add/remove fruits to/from the bags.
Clarification: I changed the wording from "you can grab $50$ bags..." to "there exist $50$ bags..."
Clarification from comments: each bag can contain any number of apples and any number of oranges with any total number of fruit; the total amount of fruit in a bag doesn't have to be the same for each bag.