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Question 10 : In a tournament, there are 43 junior level and 51 senior level participants. Each pair of juniors play one match. Each pair of seniors play one match. There is no junior versus senior match. The number of girl versus girl matches in junior level is 153, while the number of boy versus boy matches in senior level is 276. The number of matches a boy plays against a girl is [TITA]

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Given that in a tournament there are 43 junior level and 51 senior level participants, let us assume that there are n number of girls and m number of boys

The number of girl versus girl matches in junior level is 153

So ^{n}C_{2} = 153

\\frac{n(n-1)}{2}) = 153

n(n-1) = 306 = 18 × 17

There are 18 girls and 43 -18 = 25 boys.

Supposing that m boys in the senior level, ^{m}C_{2} = 276

\\frac{m(m-1)}{2}) = 276

m(m-1) = 552 = 276 × 2 = 138 × 4 = 69 × 8 = 23 × 24

In senior level there are 24 boys and 27 girls

The number of matches a boy plays against a girl has to be found

⟹ 25 × 18 + 24 × 27

⟹ 450 + 648

⟹ 1098

The number of matches a boy plays against a girl is 1098.

The question is **"In a tournament, there are 43 junior level and 51 senior level participants. Each pair of juniors play one match. Each pair of seniors play one match. There is no junior versus senior match. The number of girl versus girl matches in junior level is 153, while the number of boy versus boy matches in senior level is 276. The number of matches a boy plays against a girl is [TITA]"**

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