In a college , the ratio of the number of boys to girls is 8:5 . If there are 160 girls . Find the total number of students in the college is :

Options

A. 100
B. 250
C. 260
D. 416

Answer

To solve the problem step by step, we will use the given ratio of boys to girls and the number of girls to find the total number of students in the college.

### Step 1: Understand the Ratio
The ratio of boys to girls is given as 8:5. This means that for every 8 boys, there are 5 girls.

### Step 2: Define Variables
Let the number of boys be represented as \(8x\) and the number of girls as \(5x\), where \(x\) is a common multiplier.

### Step 3: Use the Given Information
We know that the number of girls is 160. Therefore, we can set up the equation:
\[ 5x = 160 \]

### Step 4: Solve for \(x\)
To find the value of \(x\), we divide both sides of the equation by 5:
\[ x = \frac{160}{5} = 32 \]

### Step 5: Calculate the Number of Boys
Now that we have the value of \(x\), we can find the number of boys:
\[ \text{Number of boys} = 8x = 8 \times 32 = 256 \]

### Step 6: Calculate the Total Number of Students
Now, we can find the total number of students in the college by adding the number of boys and girls:
\[ \text{Total students} = \text{Number of boys} + \text{Number of girls} = 256 + 160 = 416 \]

### Final Answer
The total number of students in the college is **416**.

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