The average age of 3 girls is 20 years and their ages are in the proportion 3:5:7 the age of youngest girl is

Options

A. 4 years
B. 6 years 8 months
C. 8 years 3 months
D. 12 years

Answer

To find the age of the youngest girl given that the average age of three girls is 20 years and their ages are in the ratio 3:5:7, we can follow these steps:

### Step 1: Calculate the total age of the girls.
The average age of the three girls is given as 20 years. Since the average is calculated by dividing the total age by the number of girls, we can find the total age as follows:

\[ \text{Total age} = \text{Average age} \times \text{Number of girls} = 20 \times 3 = 60 \text{ years} \]

### Step 2: Set up the ratio of their ages.
The ages of the girls are in the ratio 3:5:7. Let's denote the ages of the girls as \(3x\), \(5x\), and \(7x\), where \(x\) is a common multiplier.

### Step 3: Write the equation for total age.
According to the ratio, the total age can also be expressed as:

\[ 3x + 5x + 7x = 60 \]

### Step 4: Simplify the equation.
Combine the terms on the left side:

\[ 15x = 60 \]

### Step 5: Solve for \(x\).
To find \(x\), divide both sides of the equation by 15:

\[ x = \frac{60}{15} = 4 \]

### Step 6: Find the ages of the girls.
Now that we have \(x\), we can find the ages of each girl:

- Age of the youngest girl: \(3x = 3 \times 4 = 12\) years
- Age of the second girl: \(5x = 5 \times 4 = 20\) years
- Age of the oldest girl: \(7x = 7 \times 4 = 28\) years

### Conclusion:
The age of the youngest girl is **12 years**.

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