Out of 1200 students of a college, 400 played cricket, 350 played football and 512 played table tennis: of the total 100 played both cricket and football; 142 played football and table tennis; 95 played cricket and table tennis; 50 played all the three games.
(i) How many students did not play any game?
(ii) How many students played only onegame?
Answers
Given:
There are 1200 students.
400 played cricket
350 played football
512 played table tennis
100 played both cricket and football
142 played football and table tennis
95 played cricket and table tennis
50 played all the 3 games
To Find:
(1) Number of students that do not play any game
(2) Number of students that played only one game
Solution
Find the number of students that played exactly two games:
Played exactly 2 games = played at least 2 games - played 3 games
Played only cricket and football = 100 - 50
Played only cricket and football = 150
Played only football and table tennis = 142 - 50
Played only football and table tennis = 92
Played only cricket and table tennis = 95 - 50
Played only cricket and table tennis = 45
* Depicted in green in the diagram
Find the number of students that played exactly one games:
Played exactly 1 games = played the game - played exactly 2 games - played 3 games
Played only cricket = 400 - 50 - 50 - 45
Played only cricket = 225
Played only football = 350 - 50 - 50 - 92
Played only cricket = 158
Played only table tennis = 512 - 50 - 45 - 92
Played only cricket = 325
* Depicted in black in the diagram
Find the number of students that did not play any game:
Number of students that played at least 1 game = 255 + 158 + 325 + 50 = 45 + 92 + 50
Number of students that played at least 1 game = 975
Number of students that do not play any game = 1200 - 975
Number of students that do not play any game = 225
Find the number of students that played only 1 game:
Played only 1 game = 255 + 158 + 325
Played only 1 game = 738
Answer: (1) 225 students do not play any games. (2) 738 students played at least 1 game.
Answer:
(1) 225 students do not play any games
(2) 738 students played at least 1 game