Present age of father is 42 years and that of his son is 14 years. Find the ratio of
Age of father to the age of son when father was 30 years old.

Answer

To solve the problem step by step, we need to find the ratio of the father's age to the son's age when the father was 30 years old.

### Step 1: Understand the present ages
The present age of the father is 42 years, and the present age of the son is 14 years.

### Step 2: Determine how many years ago the father was 30
To find out how many years ago the father was 30, we subtract 30 from the father's current age:
- Current age of father = 42 years
- Age when father was 30 = 30 years

Years ago when father was 30:
\[ 42 - 30 = 12 \text{ years ago} \]

### Step 3: Calculate the son's age 12 years ago
Now we need to find out how old the son was 12 years ago. We subtract 12 years from the son's current age:
- Current age of son = 14 years

Son's age 12 years ago:
\[ 14 - 12 = 2 \text{ years old} \]

### Step 4: Set up the ratio of the father's age to the son's age
Now we can set up the ratio of the father's age to the son's age when the father was 30:
- Father's age when he was 30 = 30 years
- Son's age when father was 30 = 2 years

The ratio of the father's age to the son's age is:
\[ \text{Ratio} = \frac{\text{Father's age}}{\text{Son's age}} = \frac{30}{2} \]

### Step 5: Simplify the ratio
Now we simplify the ratio:
\[ \frac{30}{2} = 15 \]
So, the ratio can be expressed as:
\[ 15:1 \]

### Final Answer
The ratio of the father's age to the son's age when the father was 30 years old is:
\[ \text{Final Ratio} = 15:1 \]

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