A father’s age is four times as much as the sum of the ages of his three children but 6 years hence his age will be only double the sum of their ages. Then the age of the father is-

Options

A. 30 years
B. 40 years
C. 60 years
D. 45 years

Answer

To solve the problem regarding the ages of a father and his three children, we can follow these steps:

### Step 1: Define the Variables
Let the sum of the ages of the three children be represented as \( x \).

### Step 2: Express the Father's Age
According to the problem, the father's age is four times the sum of the ages of his children. Therefore, we can express the father's age as:
\[ \text{Father's Age} = 4x \]

### Step 3: Determine Future Ages
The problem states that in 6 years, the father's age will be double the sum of the ages of the children. In 6 years, the father's age will be:
\[ 4x + 6 \]
In 6 years, each child will also be 6 years older, so the sum of the ages of the children will be:
\[ x + 18 \quad (\text{since there are 3 children, each gaining 6 years}) \]

### Step 4: Set Up the Equation
According to the problem, in 6 years, the father's age will be double the sum of the children's ages:
\[ 4x + 6 = 2(x + 18) \]

### Step 5: Simplify the Equation
Now, we will simplify the equation:
\[ 4x + 6 = 2x + 36 \]

### Step 6: Rearrange the Equation
Next, we will rearrange the equation to isolate \( x \):
\[ 4x - 2x = 36 - 6 \]
\[ 2x = 30 \]

### Step 7: Solve for \( x \)
Now, divide both sides by 2 to find \( x \):
\[ x = 15 \]

### Step 8: Calculate the Father's Age
Now that we have \( x \), we can find the father's current age:
\[ \text{Father's Age} = 4x = 4 \times 15 = 60 \]

### Conclusion
Thus, the age of the father is:
\[ \text{Father's Age} = 60 \text{ years} \]

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