David's present age is 2/7th of his father's present age. David's brother is three year older to David. The respective ratio between present ages of David father and David's brother is 14:5 . What is the present age of David?

Options

A. 12 years
B. 23 years
C. 19 years
D. 27 years

Explanation

To solve the problem step by step, let's define the variables and use the information provided in the question.

### Step 1: Define Variables
Let:
- David's present age = \( D \)
- Father's present age = \( F \)
- David's brother's present age = \( B \)

### Step 2: Set Up Equations
From the problem, we have the following relationships:
1. David's present age is \( \frac{2}{7} \) of his father's present age:
\[ D = \frac{2}{7} F \]

2. David's brother is 3 years older than David:
\[ B = D + 3 \]

3. The ratio of the present ages of David's father and David's brother is \( 14:5 \):
\[ \frac{F}{B} = \frac{14}{5} \]
This can be rewritten as:
\[ 5F = 14B \]

### Step 3: Substitute for \( B \)
Now, substitute \( B \) from the second equation into the third equation:
\[ 5F = 14(D + 3) \]

### Step 4: Substitute for \( D \)
Now substitute \( D \) from the first equation into the equation:
\[ 5F = 14\left(\frac{2}{7}F + 3\right) \]

### Step 5: Simplify the Equation
Distributing the \( 14 \) gives:
\[ 5F = 14 \cdot \frac{2}{7}F + 42 \]
\[ 5F = 4F + 42 \]

### Step 6: Solve for \( F \)
Now, isolate \( F \):
\[ 5F - 4F = 42 \]
\[ F = 42 \]

### Step 7: Find David's Age
Now that we have \( F \), we can find \( D \):
\[ D = \frac{2}{7}F = \frac{2}{7} \cdot 42 = 12 \]

### Conclusion
David's present age is \( 12 \) years.