In a school, 50% students play cricket and 40% play football. If 10% of students play both the games, then what percent of students play neither cricket nor football?
(a)`10%`
(b)`15%`
(c)`20%`
(d)`25%`

Options

A. `10%`
B. `15%`
C. `20%`
D. `25%`

Answer

To solve the problem step by step, we will use the principle of inclusion-exclusion to find the percentage of students who play neither cricket nor football.

### Step 1: Define the percentages
Let:
- \( C \) = percentage of students who play cricket = 50%
- \( F \) = percentage of students who play football = 40%
- \( B \) = percentage of students who play both cricket and football = 10%

### Step 2: Calculate the percentage of students who play only cricket and only football
- Percentage of students who play only cricket = \( C - B = 50\% - 10\% = 40\% \)
- Percentage of students who play only football = \( F - B = 40\% - 10\% = 30\% \)

### Step 3: Calculate the total percentage of students who play at least one game
To find the total percentage of students who play either cricket or football, we add the percentages of students who play only cricket, only football, and both:
\[ \text{Total playing at least one game} = (\text{Only Cricket}) + (\text{Only Football}) + (\text{Both}) \]
\[ = 40\% + 30\% + 10\% = 80\% \]

### Step 4: Calculate the percentage of students who play neither game
To find the percentage of students who play neither cricket nor football, we subtract the total percentage of students who play at least one game from 100%:
\[ \text{Percentage playing neither} = 100\% - \text{Total playing at least one game} \]
\[ = 100\% - 80\% = 20\% \]

### Conclusion
Thus, the percentage of students who play neither cricket nor football is **20%**.

### Answer
(c) 20%

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