In a class of 100 students, 60 play cricket, 50 play Hockey and 30 play both. Then the number of students who play only one of the two game is

Options

A. 80
B. 50
C. 30
D. none of these.

Answer

To find the number of students who play only one of the two games (Cricket or Hockey), we can use the principle of inclusion-exclusion.

Let's denote:
- \( C \) = Number of students who play Cricket = 60
- \( H \) = Number of students who play Hockey = 50
- \( B \) = Number of students who play both Cricket and Hockey = 30

We need to find the number of students who play only Cricket and only Hockey.

1. **Calculate the number of students who play only Cricket:**
\[ \text{Only Cricket} = C - B = 60 - 30 = 30 \]

2. **Calculate the number of students who play only Hockey:**
\[ \text{Only Hockey} = H - B = 50 - 30 = 20 \]

3. **Total number of students who play only one game:**
\[ \text{Only one game} = \text{Only Cricket} + \text{Only Hockey} = 30 + 20 = 50 \]

Thus, the number of students who play only one of the two games is **50**.