Ratio of present ages of two persons A and B is 7:4 and after four years ratio of their ages (B:A) become 6:10 . Then find the present age of B ?

Options

A. 20 years
B. 18 years
C. 32 years
D. 26 years

Explanation

To solve the problem step by step, we will denote the present ages of persons A and B using a variable.

### Step 1: Define the Present Ages
Let the present age of A be \(7x\) and the present age of B be \(4x\), based on the given ratio of their ages which is \(7:4\).

### Step 2: Determine Their Ages After Four Years
After four years, the age of A will be:
\[ 7x + 4 \]
And the age of B will be:
\[ 4x + 4 \]

### Step 3: Set Up the Equation for the New Ratio
According to the problem, after four years, the ratio of the ages of B to A becomes \(6:10\). We can express this as:
\[ \frac{4x + 4}{7x + 4} = \frac{6}{10} \]

### Step 4: Cross-Multiply to Eliminate the Fraction
Cross-multiplying gives us:
\[ 10(4x + 4) = 6(7x + 4) \]

### Step 5: Expand Both Sides
Expanding both sides results in:
\[ 40x + 40 = 42x + 24 \]

### Step 6: Rearrange the Equation
Now, we will rearrange the equation to isolate \(x\):
\[ 40x + 40 - 24 = 42x \]
\[ 16 = 42x - 40x \]
\[ 16 = 2x \]

### Step 7: Solve for \(x\)
Dividing both sides by 2 gives:
\[ x = 8 \]

### Step 8: Find the Present Age of B
Now, we can find the present age of B:
\[ \text{Present age of B} = 4x = 4 \times 8 = 32 \]

### Final Answer
The present age of B is \(32\) years.

---