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This is a question that involves the application of the concepts of Permutations and Combinations. This wonderful question appeared in the CAT 2018 Question Paper. There are essentially many ways to solve this question. Try it yourself before looking at the video explaination to see how Rajesh solves this.
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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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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Permutation & Combination

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 ⁿC₂ = 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, ^mC₂ = 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]"

Hence, the answer is 1098

 

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