There are 100 students in a particular class. 60% students play cricket, 30% student play football and 10% student play both the games. What is the number of students who play neither cricket nor football?

Correct Option (B)

To determine the number of students who play neither cricket nor football, the principle of inclusion-exclusion is applied. The total number of students is 100.

• Percentage of students playing cricket = 60%
• Percentage of students playing football = 30%
• Percentage of students playing both games = 10%

The percentage of students playing at least one of the two games is calculated as:

P(Cricket or Football) = P(Cricket) + P(Football) - P(Cricket and Football)

P(Cricket or Football) = 60% + 30% - 10% = 90% - 10% = 80%

This indicates that 80% of the students participate in at least one of the games.

The percentage of students who play neither game is the complement of those playing at least one game:

Percentage (Neither) = Total Percentage - P(Cricket or Football)

Percentage (Neither) = $(100-80)=\mathbf{\text{20\%}}$

Since the total number of students is 100, 20% of 100 students is 20 students. Therefore, 20 students play neither cricket nor football.

Incorrect Options:

Options A (25), C (18), and D (15) are incorrect. These values do not align with the accurate application of the set theory principle of inclusion-exclusion. The correct calculation, which accounts for the overlap of students playing both games, precisely yields 20 students.