In a certain town 25% families own a phone and 15% own a car 65% own neither a phone nor a car. 2000 families own both a car and a phone. Consider the following statements in this regard
(1) 10% families own both a car and a phone
(2) 35% families own neither a car or a phone
(3) 40,000 families live in the town
Which one of these statements are correct?

Options

A. 1 and 2
B. 1 and 3
C. 2 and 3
D. 1,2 & 3

Answer

To solve the problem, we need to analyze the information given about families owning phones and cars in a town. We will use the principles of set theory and percentages to determine which statements are correct.

### Step-by-Step Solution:

1. **Identify Given Information:**
- Let \( N \) be the total number of families in the town.
- 25% of families own a phone: \( P(A) = 0.25 \)
- 15% of families own a car: \( P(B) = 0.15 \)
- 65% own neither a phone nor a car: \( P(A' \cap B') = 0.65 \)
- 2000 families own both a phone and a car: \( n(A \cap B) = 2000 \)

2. **Calculate the Probability of Families Owning Either a Phone or a Car:**
- Using the complement rule, we can find the probability of families owning either a phone or a car:
\[ P(A \cup B) = 1 - P(A' \cap B') = 1 - 0.65 = 0.35 \]

3. **Use the Formula for Union of Two Sets:**
- The formula for the union of two sets is:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
- Substituting the known values:
\[ 0.35 = 0.25 + 0.15 - P(A \cap B) \]
- Rearranging gives:
\[ P(A \cap B) = 0.25 + 0.15 - 0.35 = 0.05 \]

4. **Determine the Total Number of Families:**
- Since \( P(A \cap B) = \frac{n(A \cap B)}{N} \), we can set up the equation:
\[ 0.05 = \frac{2000}{N} \]
- Solving for \( N \):
\[ N = \frac{2000}{0.05} = 40000 \]

5. **Evaluate Each Statement:**
- **Statement 1:** 10% families own both a car and a phone.
- We found that 5% own both, so this statement is **incorrect**.
- **Statement 2:** 35% families own neither a car nor a phone.
- We found that 65% own neither, so this statement is **incorrect**.
- **Statement 3:** 40,000 families live in the town.
- We calculated that there are 40,000 families, so this statement is **correct**.

### Conclusion:
The only correct statement is **Statement 3**: 40,000 families live in the town.