Question

In a survey of 500 people, it was found that 250 owned a 4-wheeler but not a 2-wheeler, 100 owned a 2-wheeler but not a 4-wheeler, and 100 owned neither a 4-wheeler nor a 2-wheeler. Then the number of people who owned both is:

• A. 75
• B. 60
• C. 50
• D. 100

Hint:

Use Venn diagram-based reasoning to solve problems involving the union and intersection of two sets, especially when dealing with surveys and groups.

Answer 1

The Correct Option is C

Step 1: Let the number of people who owned both a 4-wheeler and a 2-wheeler be \( x \). The total number of people surveyed is 500. From the survey: - 250 people owned a 4-wheeler but not a 2-wheeler, - 100 people owned a 2-wheeler but not a 4-wheeler, - 100 people owned neither. Thus, the total number of people who owned either a 4-wheeler or a 2-wheeler is: \[ 250 + 100 + x = 500 - 100 = 400. \] Therefore: \[ 350 + x = 400 \quad \Rightarrow \quad x = 50. \] Thus, the number of people who owned both is 50. Thus, the correct answer is (C).