# In a tournament, there are 43 | Quantitative Aptitude - Modern Maths – Permutation and Combination

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The question below is from previous year CAT question from CAT 2018 exam comes from CAT Permutation and Combination: In a tournament, there are 43. Find out by answering this question which tests an aspirant’s Quantitative Ability Skills:

## CAT 2018 - Slot-2 - Arithmetic - Question-3 - In a tournament, there are 43

Q. 3:  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

Among a group of n persons, number of matches played = n(n – 1)/2 Among the Junior participants, let the number of girls be n.

The number of matches played among girls

= n(n – 1)/2 = 153

=> n(n – 1) = 306 = 18 × 17 => n = 18

Number of boys = 43 – 18 = 25

The number of matches played between a boy and a girl = 25×18 = 450 Among the Senior level participants, let the number of boys be n.

The number of matches played between two boys

= n(n – 1)/2 = 276

=> n(n – 1) = 552 = 24 × 23 => n = 24

The number of girls = 51 – 24 = 27

The number of matches played between a boy and a girl = 27 × 24 = 648 Required answer = 450 + 648 = 1098

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