In a village` 60%` families have 1 cow and, `30% ` families have 1 buffalo and`15% ` families have both 1 cow and 1 Buffalo. If there are only 96 families in a village. Find the number of families that does not have any cow or buffalo.

Answer

To solve the problem step by step, we will use the principle of inclusion-exclusion to find the number of families that do not have any cow or buffalo.

### Step 1: Calculate the number of families with cows and buffaloes
- Total families in the village = 96
- Percentage of families with cows = 60%
- Percentage of families with buffaloes = 30%
- Percentage of families with both cows and buffaloes = 15%

First, we need to find the actual number of families that have cows, buffaloes, and both.

**Number of families with cows:**
\[ \text{Families with cows} = 60\% \text{ of } 96 = \frac{60}{100} \times 96 = 57.6 \approx 58 \text{ families} \]

**Number of families with buffaloes:**
\[ \text{Families with buffaloes} = 30\% \text{ of } 96 = \frac{30}{100} \times 96 = 28.8 \approx 29 \text{ families} \]

**Number of families with both cows and buffaloes:**
\[ \text{Families with both} = 15\% \text{ of } 96 = \frac{15}{100} \times 96 = 14.4 \approx 14 \text{ families} \]

### Step 2: Use the inclusion-exclusion principle
To find the number of families that have either cows or buffaloes, we use the formula:
\[ \text{Families with cows or buffaloes} = \text{Families with cows} + \text{Families with buffaloes} - \text{Families with both} \]

Substituting the values we calculated:
\[ \text{Families with cows or buffaloes} = 58 + 29 - 14 = 73 \text{ families} \]

### Step 3: Calculate the number of families without cows or buffaloes
Now, we can find the number of families that do not have any cows or buffaloes by subtracting the number of families that have either from the total number of families:
\[ \text{Families without cows or buffaloes} = \text{Total families} - \text{Families with cows or buffaloes} \]
\[ \text{Families without cows or buffaloes} = 96 - 73 = 23 \text{ families} \]

### Final Answer
The number of families that do not have any cow or buffalo is **23 families**.

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