The average age of boys in the class is twice the number of girls in the class. The ratio of boys and girls in the class of 50 is `4:1`. The total of the ages (in years) of the boys in the class is

Options

A. 2000
B. 2500
C. 800
D. 400

Answer

To solve the problem step by step, we will follow the information given in the question and apply the concepts of ratios and averages.

### Step 1: Understand the Ratio of Boys and Girls
The ratio of boys to girls in the class is given as 4:1. This means for every 4 boys, there is 1 girl.

### Step 2: Calculate the Total Number of Boys and Girls
The total number of students in the class is 50. We can express the number of boys (B) and girls (G) using the ratio:
- Let the number of boys be 4x and the number of girls be x.
- Therefore, we have:
\[ 4x + x = 50 \]
\[ 5x = 50 \]
\[ x = 10 \]
- Now, substituting back to find the number of boys and girls:
\[ B = 4x = 4 \times 10 = 40 \quad \text{(boys)} \]
\[ G = x = 10 \quad \text{(girls)} \]

### Step 3: Determine the Average Age of Boys
The problem states that the average age of boys is twice the number of girls. Since we have found that the number of girls is 10, we can calculate the average age of boys:
- Average age of boys = 2 × Number of girls
\[ \text{Average age of boys} = 2 \times 10 = 20 \text{ years} \]

### Step 4: Calculate the Total Age of Boys
To find the total age of boys, we use the formula:
\[ \text{Total age of boys} = \text{Average age of boys} \times \text{Number of boys} \]
Substituting the values we have:
\[ \text{Total age of boys} = 20 \times 40 \]
\[ \text{Total age of boys} = 800 \text{ years} \]

### Conclusion
The total of the ages (in years) of the boys in the class is **800 years**.

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