Question

In a group of 200 Boys, 80 play Cricket, 60 play Chess and 35 play both Cricket and Chess. Number of boys play neither Cricket nor Chess is

• A. 95
• B. 90
• C. 105
• D. 85

Hint:

Using the quick formula:
\[ \text{Neither} = \text{Total} - (\text{Set A} + \text{Set B} - \text{Both}) \] \[ \text{Neither} = 200 - (80 + 60 - 35) = 200 - 105 = 95 \] Keep this simple subtraction path in mind for set theory questions.

Answer 1

The Correct Option is A

Step 1: Note the given data.
Total boys = 200. Cricket = 80, Chess = 60, Both = 35.
Step 2: Apply the inclusion-exclusion principle.
Boys playing at least one sport = n(Cricket) + n(Chess) - n(Both) = 80 + 60 - 35 = 105.
Step 3: Find boys playing neither sport.
Boys playing neither = Total - at least one = 200 - 105 = 95.
\[ \boxed{95} \]