Out of two-thirds of the total number of basket-ball matches, a team has won 17 matches and lost 3 of them. What is the maximum number of matches that the team can lose and still win three-fourths of the total number of matches, if it is true that no match can end in a tie?
The team has already played 17 (won) + 3 (lost) = 20 matches.
These constitute two-thirds of the total matches.
Thus the total number of matches is 30.
If the team is supposed to win three-fourths of these, it has to win 22.5, i.e. 23 matches in all.
There are (30 - 20) = 10 matches remaining.
So the team has to win (23 - 17) = 6 of these 10 matches, i.e. it can lose no more than (10 - 6) = 4 matches.