The ratio of A's age to B's age is `4 : 3`. 'A' will be 26 years old after 6 years. The age of B now is :

Options

A. `19(1/2)` years
B. 12 years
C. 21 years
D. 15 years

Answer

To solve the problem step by step, we will follow the given information and use the concept of ratios.

### Step 1: Understand the ratio of A's age to B's age
The ratio of A's age to B's age is given as \(4 : 3\). This means that for every 4 years of A's age, B's age is 3 years.

### Step 2: Determine A's current age
We know that A will be 26 years old after 6 years. Therefore, we can find A's current age by subtracting 6 from 26:
\[ \text{A's current age} = 26 - 6 = 20 \text{ years} \]

### Step 3: Set up the ratio
Since the ratio of A's age to B's age is \(4 : 3\), we can express A's and B's ages in terms of a common variable \(x\):
\[ \text{A's age} = 4x \quad \text{and} \quad \text{B's age} = 3x \]

### Step 4: Substitute A's current age into the equation
We know from Step 2 that A's current age is 20 years. Therefore, we can set up the equation:
\[ 4x = 20 \]

### Step 5: Solve for \(x\)
To find the value of \(x\), we divide both sides of the equation by 4:
\[ x = \frac{20}{4} = 5 \]

### Step 6: Calculate B's current age
Now that we have the value of \(x\), we can find B's current age using the expression for B's age:
\[ \text{B's age} = 3x = 3 \times 5 = 15 \text{ years} \]

### Conclusion
The current age of B is 15 years.