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, we need to determine the present age of B based on the information given. Let's break it down step by step.

### Step-by-Step Solution:

1. **Define 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.

2. **Set Up the Equation**:
- According to the problem, in 10 years, A's age will be twice the age of B 10 years ago.
- In 10 years, A's age will be \( (X + 9) + 10 = X + 19 \).
- B's age 10 years ago was \( X - 10 \).
- Therefore, the equation can be set up as:
\[ X + 19 = 2(X - 10) \]

3. **Simplify the Equation**:
- Expand the right side of the equation:
\[ X + 19 = 2X - 20 \]

4. **Rearrange the Equation**:
- Move all terms involving \( X \) to one side and constant terms to the other side:
\[ 19 + 20 = 2X - X \]
\[ 39 = X \]

5. **Conclusion**:
- The present age of B is \( X = 39 \) years.

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

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