In a group of 110 students, 23 students did not participate in any of the two games: Badminton and Chess. 45 students participated in Badminton and 61 students participated in Chess. How many students participated in Badminton only?

26

THE LOGIC;

Let's denote the number of students who participated in both Badminton and Chess as (x). The total number of students who participated in Badminton is 45, and the total number of students who participated in Chess is 61.

The number of students who participated in at least one of the games can be expressed as the sum of those who participated in Badminton only, Chess only, and both games.

Total participating students = Badminton only + Chess only + Both

Given that there are 110 students in total and 23 students did not participate in any of the two games, we can write the equation:-

$110-23=(45-x)+(61-x)+x$

Solving for (x):

87 = 106 − x

x = 106−87

x=19

Now, to find the number of students who participated in Badminton only, subtract the number of students who participated in both games from the total number of Badminton participants:

Badminton only = 45 − x = 45 − 19 = 26 

Thus, the correct answer is 26.