Question

Read the information given below and answer the question that follows.
Ten teams participated in a hockey tournament, in which every team played every other team once. After the tournament was over, it was found that the ten teams could be divided into 2 groups A and B, such that every team in A won against every team in B and every team in A won the same number of matches.
If there were altogether 10 matches played among the teams of B, how many matches did each team in A win?

पर्याय

• 5

• 6

• 7

• 8

Answer 1

If there were p teams in B, number of matches played within B = p (p - 1)/2 = 10
∴ p = 5
So, there are 5 teams in A and the number of matches played within A is `""^5C_2` i.e., 10, of which each team won 2. Since each team in A won the 5 matches against teams in B, each team in A won 7 matches.
So, 7 is the correct option.