Each family in Gyanpur village has atmost two adults and the total number of boys in this village is less than the number of girls. Similarly the number of girls is less than the number of adults in the village. Raghubir Singh, the chief of this village is the only adult in his family. The minimum number of families in his village is:

Options

A. 2
B. 3
C. 4
D. none of these

Answer

To solve the problem, we need to analyze the given conditions step by step.

### Step 1: Understand the conditions
1. Each family has at most two adults.
2. The total number of boys is less than the total number of girls.
3. The total number of girls is less than the total number of adults in the village.
4. Raghubir Singh is the only adult in his family.

### Step 2: Start with the minimum number of families
Let's assume the minimum number of families is 2.

- **Family 1**: Raghubir Singh (1 adult, 1 boy or girl).
- **Family 2**: If we assume this family has 2 adults, they could be two females or one male and one female.

### Step 3: Check the conditions with 2 families
1. **Number of boys**: If Family 1 has 1 boy and Family 2 has 1 boy, then total boys = 2.
2. **Number of girls**: If Family 1 has 1 girl and Family 2 has 2 girls, then total girls = 3.
3. **Total adults**: Raghubir Singh + 2 adults from Family 2 = 3 adults.

Now, we check the conditions:
- Number of boys (2) < Number of girls (3) - **Condition satisfied**.
- Number of girls (3) < Number of adults (3) - **Condition not satisfied**.

Since the conditions are not satisfied with 2 families, we need to check with 3 families.

### Step 4: Assume there are 3 families
- **Family 1**: Raghubir Singh (1 adult, 1 child - can be a boy or girl).
- **Family 2**: 2 adults (let's assume both are females).
- **Family 3**: 2 adults (1 male and 1 female).

### Step 5: Count the members
1. **Family 1**: 1 adult (Raghubir Singh) + 1 child (assume 1 boy).
2. **Family 2**: 2 adults (2 females).
3. **Family 3**: 2 adults (1 male, 1 female).

Now, let's count:
- **Total boys**: 1 (from Family 1) + 1 (from Family 3) = 2 boys.
- **Total girls**: 2 (from Family 2) + 1 (from Family 3) = 3 girls.
- **Total adults**: 1 (Raghubir Singh) + 2 (Family 2) + 2 (Family 3) = 5 adults.

### Step 6: Check the conditions
- Number of boys (2) < Number of girls (3) - **Condition satisfied**.
- Number of girls (3) < Number of adults (5) - **Condition satisfied**.

Since all conditions are satisfied with 3 families, we conclude that the minimum number of families in Gyanpur village is **3**.

### Final Answer
The minimum number of families in Gyanpur village is **3**.

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