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  • A sporting event has 20 junior and 30 senior-level participants. Each junior pair competes in one match. Each senior pair competes in one match. There will be no junior versus senior matc

A sporting event has 20 junior and 30 senior-level participants. Each junior pair competes in one match. Each senior pair competes in one match. There will be no junior versus senior match. The number of junior-level girl versus girl matches is 105, while the number of senior-level boy versus-boy matches is 171. How many matches does a boy play against a girl?

 

Option: 1

284


Option: 2

209


Option: 3

282


Option: 4

210


Answers (1)

best_answer

The total number of matches is   \mathrm{^2^0C_2+^3^0C_2=625.}

Junior-level girl vs. girl matches is,

\mathrm{\frac{n\left ( n-1 \right )}{2}=105}

\mathrm{n=15}

Thus, the number of girls equals 15.

So the number of junior boys is 20 - 15 = 5.

The number of matches played between a boy and a girl in the junior level is 5\times 15=75.

Senior-level boy versus boy matches is,

\mathrm{\frac{n\left ( n-1 \right )}{2}=171}

\mathrm{n=19}

So the number of senior boys is 19.

The number of senior girls is 30 - 19 = 11.

The number of matches played between a boy and a girl at the senior level is \mathrm{11\times 19=209.}

Therefore, the total number of girl versus boy matches is \mathrm{75+209=284.} 

 

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Riya

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