Question

In a town, 65% of people watched the news on television, 40% read a newspaper and 25% read a newspaper and watched the news on television also. What percent of people neither watched the news on television nor read a newspaper?

• A. 5
• B. 10
• C. 15
• D. 20
• E. 25

Hint:

Use formula: \[ A + B - (A \cap B) \] for two-set problems.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Use the Set Theory formula: $n(A \cup B) = n(A) + n(B) - n(A \cap B)$.
Step 2: Detailed Explanation:
Let TV watchers be $T$ and Newspaper readers be $N$. $n(T) = 65%$ $n(N) = 40%$ $n(T \cap N) = 25%$
Step 3: Calculation:
Percentage of people doing at least one activity: $n(T \cup N) = 65 + 40 - 25 = 80%$ Percentage of people doing neither = $100% - 80% = 20%$.
Step 4: Final Answer:
The percentage of people who did neither is 20%. Thus, the correct option is (d).