Question

A chess tournament is conducted for students of age 11 and 12 only. The total participants were 280. The sum of the ages of all the students was 3238 years. How many 11 year old students participated at the chess tournament?
(1)55 (2) 132 (3) 158 (4)122​

Answer 1

Let the number of participants be x

Let the number of participants be xIf no participant fell ill, then number of games played =nC2

Let the number of participants be xIf no participant fell ill, then number of games played =nC2Each player will play n−1 games in the tournament

Let the number of participants be xIf no participant fell ill, then number of games played =nC2Each player will play n−1 games in the tournamentThere n−1 games most include 1 game which should be played by the player with other.

Let the number of participants be xIf no participant fell ill, then number of games played =nC2Each player will play n−1 games in the tournamentThere n−1 games most include 1 game which should be played by the player with other.No. of games played =nC2−[(n−1)+(n−1)−1]+6=84

Let the number of participants be xIf no participant fell ill, then number of games played =nC2Each player will play n−1 games in the tournamentThere n−1 games most include 1 game which should be played by the player with other.No. of games played =nC2−[(n−1)+(n−1)−1]+6=84⇒2(n−1)n−[n−1+n−1−1]+6=84

Let the number of participants be xIf no participant fell ill, then number of games played =nC2Each player will play n−1 games in the tournamentThere n−1 games most include 1 game which should be played by the player with other.No. of games played =nC2−[(n−1)+(n−1)−1]+6=84⇒2(n−1)n−[n−1+n−1−1]+6=84⇒2(n−1)n−2n+3+6=84

Let the number of participants be xIf no participant fell ill, then number of games played =nC2Each player will play n−1 games in the tournamentThere n−1 games most include 1 game which should be played by the player with other.No. of games played =nC2−[(n−1)+(n−1)−1]+6=84⇒2(n−1)n−[n−1+n−1−1]+6=84⇒2(n−1)n−2n+3+6=84⇒2(n−1)n−2n+9=84

Let the number of participants be xIf no participant fell ill, then number of games played =nC2Each player will play n−1 games in the tournamentThere n−1 games most include 1 game which should be played by the player with other.No. of games played =nC2−[(n−1)+(n−1)−1]+6=84⇒2(n−1)n−[n−1+n−1−1]+6=84⇒2(n−1)n−2n+3+6=84⇒2(n−1)n−2n+9=84⇒2(n2−n)−2n+9=84

Let the number of participants be xIf no participant fell ill, then number of games played =nC2Each player will play n−1 games in the tournamentThere n−1 games most include 1 game which should be played by the player with other.No. of games played =nC2−[(n−1)+(n−1)−1]+6=84⇒2(n−1)n−[n−1+n−1−1]+6=84⇒2(n−1)n−2n+3+6=84⇒2(n−1)n−2n+9=84⇒2(n2−n)−2n+9=84⇒n2−5n−150=0

Let the number of participants be xIf no participant fell ill, then number of games played =nC2Each player will play n−1 games in the tournamentThere n−1 games most include 1 game which should be played by the player with other.No. of games played =nC2−[(n−1)+(n−1)−1]+6=84⇒2(n−1)n−[n−1+n−1−1]+6=84⇒2(n−1)n−2n+3+6=84⇒2(n−1)n−2n+9=84⇒2(n2−n)−2n+9=84⇒n2−5n−150=0⇒n2+10n+15n−150=0

Let the number of participants be xIf no participant fell ill, then number of games played =nC2Each player will play n−1 games in the tournamentThere n−1 games most include 1 game which should be played by the player with other.No. of games played =nC2−[(n−1)+(n−1)−1]+6=84⇒2(n−1)n−[n−1+n−1−1]+6=84⇒2(n−1)n−2n+3+6=84⇒2(n−1)n−2n+9=84⇒2(n2−n)−2n+9=84⇒n2−5n−150=0⇒n2+10n+15n−150=0⇒n(n+10)−15(n+10)=0

Let the number of participants be xIf no participant fell ill, then number of games played =nC2Each player will play n−1 games in the tournamentThere n−1 games most include 1 game which should be played by the player with other.No. of games played =nC2−[(n−1)+(n−1)−1]+6=84⇒2(n−1)n−[n−1+n−1−1]+6=84⇒2(n−1)n−2n+3+6=84⇒2(n−1)n−2n+9=84⇒2(n2−n)−2n+9=84⇒n2−5n−150=0⇒n2+10n+15n−150=0⇒n(n+10)−15(n+10)=0⇒(n+10)(n−15)=0

Let the number of participants be xIf no participant fell ill, then number of games played =nC2Each player will play n−1 games in the tournamentThere n−1 games most include 1 game which should be played by the player with other.No. of games played =nC2−[(n−1)+(n−1)−1]+6=84⇒2(n−1)n−[n−1+n−1−1]+6=84⇒2(n−1)n−2n+3+6=84⇒2(n−1)n−2n+9=84⇒2(n2−n)−2n+9=84⇒n2−5n−150=0⇒n2+10n+15n−150=0⇒n(n+10)−15(n+10)=0⇒(n+10)(n−15)=0n=10 [Not possible]

Let the number of participants be xIf no participant fell ill, then number of games played =nC2Each player will play n−1 games in the tournamentThere n−1 games most include 1 game which should be played by the player with other.No. of games played =nC2−[(n−1)+(n−1)−1]+6=84⇒2(n−1)n−[n−1+n−1−1]+6=84⇒2(n−1)n−2n+3+6=84⇒2(n−1)n−2n+9=84⇒2(n2−n)−2n+9=84⇒n2−5n−150=0⇒n2+10n+15n−150=0⇒n(n+10)−15(n+10)=0⇒(n+10)(n−15)=0n=10 [Not possible]n=