The average age of three boys is 15 years if their ages are in the ratio 3:5:7 the age of the youngest boy is

Options

A. 9 years
B. 15 years
C. 18 years
D. 21 years

Answer

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

### Step 1: Understand the given information
We know that the average age of three boys is 15 years and their ages are in the ratio of 3:5:7.

### Step 2: Set up the expressions for their ages
Let the ages of the three boys be represented as:
- Youngest boy (A) = 3X
- Middle boy (B) = 5X
- Oldest boy (C) = 7X

### Step 3: Calculate the total age using the average
Since the average age of the three boys is given as 15 years, we can use the formula for average:
\[ \text{Average} = \frac{\text{Sum of ages}}{\text{Number of boys}} \]
Substituting the values we have:
\[ 15 = \frac{3X + 5X + 7X}{3} \]

### Step 4: Simplify the equation
Combine the terms in the numerator:
\[ 15 = \frac{15X}{3} \]

### Step 5: Solve for X
Multiply both sides by 3 to eliminate the denominator:
\[ 15 \times 3 = 15X \]
\[ 45 = 15X \]
Now, divide both sides by 15:
\[ X = \frac{45}{15} = 3 \]

### Step 6: Find the age of the youngest boy
Now that we have the value of X, we can find the age of the youngest boy:
\[ \text{Age of youngest boy} = 3X = 3 \times 3 = 9 \text{ years} \]

### Final Answer
The age of the youngest boy is **9 years**.

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