In `10` years, `A` will be twice as old as `B` was `10` years ago. If at present `A` is `9` years older than `B`, then present age of `B` is `:`

Options

A. `19` years
B. `29` years
C. `39` years
D. `49` years

Explanation

To solve the problem step by step, we will define the variables and set up the equations based on the information provided in the question.

### Step 1: Define the Variables
Let the present age of B be \( X \) years. Since A is 9 years older than B, the present age of A will be \( X + 9 \) years.

### Step 2: Determine Future and Past Ages
In 10 years, the age of A will be:
\[ A + 10 = (X + 9) + 10 = X + 19 \text{ years} \]
10 years ago, the age of B was:
\[ B - 10 = X - 10 \text{ years} \]

### Step 3: Set Up the Equation
According to the problem, in 10 years, A will be twice as old as B was 10 years ago. Therefore, we can set up the equation:
\[ X + 19 = 2(X - 10) \]

### Step 4: Solve the Equation
Now, we will solve the equation:
\[ X + 19 = 2X - 20 \]
Rearranging gives:
\[ 19 + 20 = 2X - X \]
\[ 39 = X \]

### Step 5: Conclusion
Thus, the present age of B is:
\[ \text{Present age of B} = X = 39 \text{ years} \]

### Final Answer
The present age of B is **39 years**.

---