Team 'A' consists of 7 boys and n girls and Team 'B' has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then n is equal to :

Solution

Maths sir · 3 steps

Every boy of A meets every boy of B, and every girl of A meets every girl of B, so multiply.

1. Boy matches. Each of the 7 boys in Team A can play each of the 4 boys in Team B. That gives 7 × 4 = 28 matches.
2. Girl matches. Each of the n girls in Team A can play each of the 6 girls in Team B. That gives 6n matches.

   28 + 6n = 52 ⇒ 6n = 24 ⇒ n = 4

3. So. Team A has 4 girls, which is option (c).

The idea to keep. A match picks one player from each team, so the count is a product. Add the products for separate categories (boys, girls) because those cases never overlap.

Answer from the NTA final answer key. Solution by PrepWiser.