The boys and girls in a school are in the the ratio `8 : 5`. If the number of girls is 160. What is the total strength of the school ?

Options

A. 250
B. 260
C. 356
D. 256

Answer

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

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

### Step 2: Set Up the Equation
Let the number of boys be represented by \( x \). We know the number of girls is 160. According to the ratio, we can set up the equation:
\[ \frac{x}{160} = \frac{8}{5} \]

### Step 3: Cross Multiply
To solve for \( x \), we will cross multiply:
\[ 5x = 8 \times 160 \]

### Step 4: Calculate the Right Side
Now calculate \( 8 \times 160 \):
\[ 8 \times 160 = 1280 \]
So, the equation becomes:
\[ 5x = 1280 \]

### Step 5: Solve for \( x \)
Now, divide both sides by 5 to find \( x \):
\[ x = \frac{1280}{5} = 256 \]

### Step 6: Find the Total Strength of the School
Now that we have the number of boys (256) and the number of girls (160), we can find the total strength of the school:
\[ \text{Total Strength} = \text{Number of Boys} + \text{Number of Girls} = 256 + 160 = 416 \]

### Final Answer
The total strength of the school is **416**.

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