In a survey of a town, it was found that 65% of the people surveyed watch the news on T.V., 40% read a newspaper and 25% read a newspaper and watch the news on T.V. What per cent of the people surveyed neither watch the news on T.V. nor read a newspaper?

Options

A. `5%`
B. `10%`
C. `20%`
D. `15%`

Explanation

To solve the problem step by step, we will use the information provided in the question and apply the principle of inclusion-exclusion.

### Step 1: Define the given percentages
- Let \( A \) be the percentage of people who watch the news on TV: \( A = 65\% \)
- Let \( B \) be the percentage of people who read a newspaper: \( B = 40\% \)
- Let \( C \) be the percentage of people who both watch TV and read a newspaper: \( C = 25\% \)

### Step 2: Use the inclusion-exclusion principle
To find the percentage of people who either watch TV or read a newspaper (or both), we can use the formula:
\[ \text{Percentage of A or B} = A + B - C \]
Substituting the values:
\[ \text{Percentage of A or B} = 65\% + 40\% - 25\% \]

### Step 3: Calculate the percentage of people who watch TV or read a newspaper
\[ \text{Percentage of A or B} = 65\% + 40\% - 25\% = 80\% \]

### Step 4: Find the percentage of people who neither watch TV nor read a newspaper
To find the percentage of people who neither watch TV nor read a newspaper, we subtract the percentage of people who watch TV or read a newspaper from 100%:
\[ \text{Percentage of neither A nor B} = 100\% - \text{Percentage of A or B} \]
Substituting the calculated value:
\[ \text{Percentage of neither A nor B} = 100\% - 80\% = 20\% \]

### Conclusion
Thus, the percentage of people surveyed who neither watch the news on TV nor read a newspaper is **20%**.

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