The average of the age of Sonu, Hari and Govind is 30 years. If their ages are in the ratio of `4:5:6` respectively, then the difference between the age of Sonu and Govind is:

Options

A. A)18 years
B. B)21 years
C. C)15 years
D. D)12 years

Answer

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

### Step 1: Understand the given information
We know that:
- The average age of Sonu, Hari, and Govind is 30 years.
- Their ages are in the ratio of 4:5:6.

### Step 2: Calculate the total age
The average age of the three individuals is given as 30 years. To find the total age, we can use the formula:
\[ \text{Total Age} = \text{Average Age} \times \text{Number of Individuals} \]
Substituting the values:
\[ \text{Total Age} = 30 \times 3 = 90 \text{ years} \]

### Step 3: Set up the ratio
Let the ages of Sonu, Hari, and Govind be represented as:
- Sonu's age = \(4x\)
- Hari's age = \(5x\)
- Govind's age = \(6x\)

### Step 4: Write the equation for total age
According to the ratio, we can express the total age as:
\[ 4x + 5x + 6x = 90 \]
This simplifies to:
\[ 15x = 90 \]

### Step 5: Solve for \(x\)
To find the value of \(x\), we divide both sides of the equation by 15:
\[ x = \frac{90}{15} = 6 \]

### Step 6: Calculate individual ages
Now that we have \(x\), we can find the individual ages:
- Sonu's age = \(4x = 4 \times 6 = 24\) years
- Hari's age = \(5x = 5 \times 6 = 30\) years
- Govind's age = \(6x = 6 \times 6 = 36\) years

### Step 7: Find the difference between Sonu's and Govind's ages
The difference between Sonu's and Govind's ages is:
\[ \text{Difference} = \text{Govind's age} - \text{Sonu's age} = 36 - 24 = 12 \text{ years} \]

### Final Answer
The difference between the age of Sonu and Govind is **12 years**.

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