The ratio of number of children, women and men in colony is 6 : 4 : 3 respectively and the colony has at least 200 members. What will be minimum number of children in the colony?

Options

A. A)48
B. B)72
C. C)64
D. D)96

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the Ratio
The ratio of the number of children, women, and men in the colony is given as 6:4:3. This means for every 6 children, there are 4 women and 3 men.

### Step 2: Calculate the Total Parts in the Ratio
To find the total number of parts in the ratio, we add the parts together:
- Children: 6 parts
- Women: 4 parts
- Men: 3 parts

Total parts = 6 + 4 + 3 = 13 parts

### Step 3: Determine the Minimum Total Members
The problem states that the colony has at least 200 members. To find the minimum number of members that fits the ratio, we need to find the smallest multiple of 13 that is greater than or equal to 200.

### Step 4: Find the Smallest Multiple of 13 Greater than 200
To find the smallest multiple of 13 that is greater than or equal to 200, we can divide 200 by 13:
- 200 ÷ 13 ≈ 15.38

Since we need a whole number, we round up to the next whole number, which is 16. Now we multiply 16 by 13 to find the total number of members:
- 16 × 13 = 208

### Step 5: Calculate the Number of Children
Now that we know the total number of members is 208, we can find the number of children. Since children represent 6 parts of the total 13 parts, we calculate:
- Number of children = (6/13) × 208

### Step 6: Perform the Calculation
Now we perform the calculation:
- Number of children = (6/13) × 208 = 96

### Conclusion
The minimum number of children in the colony is **96**.