Number of boys in a school is 1200 and the number of girls is 800. Find the ratio of the number of boys to that of girls in the simplest form.

Answer

To find the ratio of the number of boys to that of girls in the simplest form, we can follow these steps:

### Step 1: Identify the numbers
We know that:
- Number of boys = 1200
- Number of girls = 800

### Step 2: Write the ratio
The ratio of boys to girls can be written as:
\[ \text{Ratio} = \frac{\text{Number of boys}}{\text{Number of girls}} = \frac{1200}{800} \]

### Step 3: Simplify the ratio
To simplify the ratio, we can divide both the numerator and the denominator by their Highest Common Factor (HCF).

### Step 4: Find the HCF
The HCF of 1200 and 800 can be calculated.
- The factors of 1200 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 48, 60, 75, 100, 120, 150, 200, 300, 400, 600, 1200
- The factors of 800 are: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400, 800

The highest common factor is 400.

### Step 5: Divide both numbers by the HCF
Now we divide both the numerator and the denominator by 400:
\[ \frac{1200 \div 400}{800 \div 400} = \frac{3}{2} \]

### Step 6: Write the final ratio
Thus, the ratio of the number of boys to the number of girls in simplest form is:
\[ 3:2 \]

### Final Answer
Hence, the required ratio is \( 3:2 \).

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