There were two women participating in a chess tournament. Every participant played two games with the other participants. The number of games that the men played between themselves proved to exceed by 66 the number of games that the men played with the women. The number of participants, is

There were two women participating in a chess tournament. Every participant played two games with the other participants. The number of games that the men played between themselves proved to exceed by 66 the number of games that the men played with the women. The number of participants, is

A
6
B
11
C
13
D
none of these

Solution:

Let there be $' n'$ men participants. Then, the number of games that the men play between themselves is

2 ${}^{n}C_{2}$ and the number of games that the men played with the women is 2. $(2 n) .$

$∴$ $2 . {}^{n}C_{2} - 2 n = 66 \Rightarrow n^{2} - 5 n - 66 = 0 \Rightarrow n = 11 .$

$∴$ Number of participants $= 11$ men + 2 women $= 13 .$

Related content

Technical Courses After 12th – Eligibility, Duration, Salary, Top Colleges

Sikkim NEET UG Merit List 2023

How to Start Preparing for NEET From Class 10?

UP NEET UG Merit List 2023

Sound Waves Mind Map for JEE, NEET and CBSE

Does Infinity Learn Institute Prepare You for JEE, NEET?

Top 5 Reasons To Study Science After Class 10th

Application for Teaching Job

Railway Jobs After 10th

CBSE Class 12 Computer Science Answer Key and Paper Analysis 2024 – Student Feedback and Expert View