After five years the age of a father will be thrice the age of his son whereas five years ago, he was seven times as old as his son was. What is father’s present age ?

Options

A. 35years
B. 40 years
C. 45 years
D. 50 years

Answer

To solve the problem step by step, we will define the variables and set up equations based on the information given in the question.

### Step 1: Define the variables
Let the present age of the son be \( x \) years.

### Step 2: Express the father's present age
According to the problem, five years ago, the father was seven times as old as his son. Therefore, the father's age five years ago can be expressed as:
- Father's age five years ago = \( 7x \)

To find the father's present age, we add 5 years:
- Father's present age = \( 7x + 5 \)

### Step 3: Express the son's age five years from now
In five years, the son's age will be:
- Son's age in five years = \( x + 5 \)

### Step 4: Set up the equation based on future ages
According to the problem, after five years, the father's age will be three times the son's age. Therefore, we can set up the equation:
\[ 7x + 10 = 3(x + 5) \]

### Step 5: Simplify the equation
Now, let's simplify the equation:
\[ 7x + 10 = 3x + 15 \]

### Step 6: Solve for \( x \)
Rearranging the equation gives:
\[ 7x - 3x = 15 - 10 \]
\[ 4x = 5 \]
\[ x = \frac{5}{4} = 1.25 \]

### Step 7: Find the father's present age
Now, substituting \( x \) back into the expression for the father's present age:
\[ \text{Father's present age} = 7x + 5 = 7(1.25) + 5 = 8.75 + 5 = 13.75 \]

### Step 8: Conclusion
The father's present age is \( 13.75 \) years.