Persons who read news paper of type A is `63%` and those who read news paper of type B is `78%`, Find `%` of people who read both newspapers

Answer

To solve the problem of finding the percentage of people who read both newspapers (type A and type B), we can use the principle of inclusion-exclusion in set theory.

### Step-by-Step Solution:

1. **Define the Variables:**
- Let \( N_A \) be the percentage of people who read newspaper A, which is given as \( N_A = 63\% \).
- Let \( N_B \) be the percentage of people who read newspaper B, which is given as \( N_B = 78\% \).
- Let \( N_{A \cap B} \) be the percentage of people who read both newspapers.

2. **Use the Inclusion-Exclusion Principle:**
- According to the inclusion-exclusion principle, the union of two sets can be expressed as:
\[ N_{A \cup B} = N_A + N_B - N_{A \cap B} \]
- Here, \( N_{A \cup B} \) represents the percentage of people who read at least one of the newspapers. Since it is not possible for more than 100% of people to read newspapers, we have:
\[ N_{A \cup B} = 100\% \]

3. **Substitute the Known Values:**
- Plugging in the values we have:
\[ 100 = 63 + 78 - N_{A \cap B} \]

4. **Simplify the Equation:**
- Combine the percentages:
\[ 100 = 141 - N_{A \cap B} \]

5. **Solve for \( N_{A \cap B} \):**
- Rearranging the equation gives:
\[ N_{A \cap B} = 141 - 100 \]
- Therefore:
\[ N_{A \cap B} = 41\% \]

### Final Answer:
The percentage of people who read both newspapers is \( 41\% \).

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