The average age of 3 children of Arihant singh is 12 years and their ratio of ages is 3:4:5 The average age of the youngest and eldest child is if he had only 3 chidren:

Options

A. 12
B. 21
C. 8
D. 9

Answer

To solve the problem step by step, we will follow the information given and perform calculations accordingly.

### Step 1: Calculate the Total Age of the Children
Given that the average age of the three children is 12 years, we can find the total age of the children.

\[ \text{Total Age} = \text{Average Age} \times \text{Number of Children} = 12 \times 3 = 36 \text{ years} \]

**Hint for Step 1:** Remember that the total age can be found by multiplying the average age by the number of individuals.

### Step 2: Set Up the Ratio of Ages
The ages of the children are in the ratio of 3:4:5. We can express their ages in terms of a variable \(x\):

- Youngest child: \(3x\)
- Middle child: \(4x\)
- Eldest child: \(5x\)

### Step 3: Write the Equation for Total Age
Now, we can set up an equation based on the total age we calculated:

\[ 3x + 4x + 5x = 36 \]

### Step 4: Combine Like Terms
Combine the terms on the left side of the equation:

\[ 12x = 36 \]

### Step 5: Solve for \(x\)
Now, divide both sides by 12 to find \(x\):

\[ x = \frac{36}{12} = 3 \]

### Step 6: Calculate the Ages of Each Child
Now that we have \(x\), we can find the ages of each child:

- Youngest child: \(3x = 3 \times 3 = 9 \text{ years}\)
- Middle child: \(4x = 4 \times 3 = 12 \text{ years}\)
- Eldest child: \(5x = 5 \times 3 = 15 \text{ years}\)

### Step 7: Calculate the Average Age of the Youngest and Eldest Child
To find the average age of the youngest and eldest child, we add their ages and divide by 2:

\[ \text{Average Age} = \frac{\text{Youngest Age} + \text{Eldest Age}}{2} = \frac{9 + 15}{2} = \frac{24}{2} = 12 \text{ years} \]

### Final Answer
The average age of the youngest and eldest child is **12 years**.

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