Q.60
25 persons are in a room. 15 of them play hockey, 17 of them play football
and 10 of them play both hockey and football.
Then the number of persons playing neither hockey nor football is
Options:
(A) 2
(B) 17
(C) 13
(D) 3
Number of Persons Playing Neither Hockey nor Football
Questions based on set theory and Venn diagrams are
frequently asked in competitive exams such as SSC, Banking, CAT, and other aptitude tests.
This problem involves calculating the number of people who do not participate in any given activity.
Given Data
- Total number of persons in the room = 25
- Persons playing hockey = 15
- Persons playing football = 17
- Persons playing both hockey and football = 10
Concept Used
For two overlapping sets, the formula used is:
n(H ∪ F) = n(H) + n(F) − n(H ∩ F)
where H represents hockey players and F represents football players.
Step-by-Step Solution
Step 1: Calculate the number of persons playing at least one game.
n(H ∪ F) = 15 + 17 − 10 = 22
Step 2: Calculate the number of persons playing neither game.
Persons playing neither = Total persons − n(H ∪ F)
= 25 − 22 = 3
Correct Answer
Option (D): 3
Conclusion
Using basic set theory principles, the number of persons who play
neither hockey nor football is:
3
