Out of 100 families in the neigh bourhood, 50 have radios. 75 have TVs and 25 have VCRs. Only 10 families have all three and each VCR owner also has a TV. If some families have radio only, how many have only TV? `(A) 30` `(B) 35` `(C) 40` `(D) 45`

Options

A. 30
B. 35
C. 40
D. 45

Explanation

To solve the problem, we will break it down step by step.

### Step-by-Step Solution:

1. **Identify the total number of families and the number of families with each device:**
- Total families (F) = 100
- Families with radios (R) = 50
- Families with TVs (T) = 75
- Families with VCRs (V) = 25
- Families with all three devices (R ∩ T ∩ V) = 10

2. **Understand the relationship between VCR and TV owners:**
- It is given that each VCR owner also has a TV. Therefore, all 25 families that own VCRs also own TVs.

3. **Calculate the number of families that have only TVs:**
- Since all VCR owners (25 families) have TVs, we can subtract these from the total number of TV owners (75 families).
- Families with TVs excluding VCR owners = T - V = 75 - 25 = 50 families.

4. **Subtract families that have all three devices from those who have only TVs:**
- Among the 50 families that have TVs (excluding VCR owners), we need to subtract the families that have all three devices (10 families).
- Families with only TVs = 50 - 10 = 40 families.

5. **Conclusion:**
- Therefore, the number of families that have only TVs is 40.

### Final Answer:
The number of families that have only TVs is **40**.