40% of the people read newspaper X, 50% read newspaper Y and 10% read both the papers. What percentage of the people read neither newspaper?

Options

A. 0.1
B. 0.15
C. 0.2
D. 0.25

Answer

To solve the problem, we can use the principle of inclusion-exclusion in set theory. Let's break it down step by step.

### Step 1: Identify the given data
- Percentage of people who read newspaper X = 40%
- Percentage of people who read newspaper Y = 50%
- Percentage of people who read both newspapers = 10%

### Step 2: Calculate the percentage of people who read at least one newspaper
To find the percentage of people who read at least one of the newspapers (X or Y), we can use the formula:
\[ \text{Percentage of people reading at least one newspaper} = P(X) + P(Y) - P(X \cap Y) \]
Where:
- \( P(X) \) = Percentage reading newspaper X
- \( P(Y) \) = Percentage reading newspaper Y
- \( P(X \cap Y) \) = Percentage reading both newspapers

Substituting the values:
\[ P(X \cup Y) = 40\% + 50\% - 10\% = 80\% \]

### Step 3: Calculate the percentage of people who read neither newspaper
To find the percentage of people who read neither newspaper, we subtract the percentage of people who read at least one newspaper from 100%:
\[ \text{Percentage of people reading neither} = 100\% - P(X \cup Y) \]
Substituting the value we found:
\[ \text{Percentage of people reading neither} = 100\% - 80\% = 20\% \]

### Step 4: Final answer
Thus, the percentage of people who read neither newspaper is:
\[ \text{20\%} \]

### Conclusion
The answer is 20%, which corresponds to option 3 (0.20).

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