The ages of A and B are in the ratio `4:3` After 6 years. Their ages will be in the ratio `11:9`, as present age is

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the present ages of A and B
Let the present age of A be \(4x\) and the present age of B be \(3x\), where \(x\) is a common multiplier.

### Step 2: Write the equation for their ages after 6 years
After 6 years, the age of A will be \(4x + 6\) and the age of B will be \(3x + 6\).

### Step 3: Set up the ratio equation
According to the problem, after 6 years, the ratio of their ages will be \(11:9\). Therefore, we can write the equation:
\[ \frac{4x + 6}{3x + 6} = \frac{11}{9} \]

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 9(4x + 6) = 11(3x + 6) \]

### Step 5: Expand both sides
Expanding both sides, we get:
\[ 36x + 54 = 33x + 66 \]

### Step 6: Rearrange the equation
Now, we will rearrange the equation to isolate \(x\):
\[ 36x - 33x = 66 - 54 \]
\[ 3x = 12 \]

### Step 7: Solve for \(x\)
Dividing both sides by 3 gives:
\[ x = 4 \]

### Step 8: Find the present ages of A and B
Now we can find the present ages:
- Age of A: \(4x = 4 \times 4 = 16\)
- Age of B: \(3x = 3 \times 4 = 12\)

### Final Answer
The present age of A is 16 years and the present age of B is 12 years.

---