A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, find the number of blue balls in the bag.

Options

A. `10`
B. `11`
C. `13`
D. `12`

Explanation

To solve the problem, we need to find the number of blue balls in the bag, given that the probability of drawing a blue ball is double that of drawing a red ball.

### Step-by-Step Solution:

1. **Identify the Variables**:
- Let the number of blue balls be \( b \).
- The number of red balls is given as \( 5 \).

2. **Calculate the Total Number of Balls**:
- The total number of balls in the bag is \( 5 + b \).

3. **Find the Probability of Drawing a Red Ball**:
- The probability of drawing a red ball is given by the formula:
\[ P(\text{Red}) = \frac{\text{Number of Red Balls}}{\text{Total Number of Balls}} = \frac{5}{5 + b} \]

4. **Find the Probability of Drawing a Blue Ball**:
- The probability of drawing a blue ball is given by:
\[ P(\text{Blue}) = \frac{\text{Number of Blue Balls}}{\text{Total Number of Balls}} = \frac{b}{5 + b} \]

5. **Set Up the Relationship Between the Probabilities**:
- According to the problem, the probability of drawing a blue ball is double that of drawing a red ball:
\[ P(\text{Blue}) = 2 \times P(\text{Red}) \]
- Substituting the probabilities we found:
\[ \frac{b}{5 + b} = 2 \times \frac{5}{5 + b} \]

6. **Simplify the Equation**:
- Multiply both sides by \( 5 + b \) to eliminate the denominator:
\[ b = 2 \times 5 \]
- This simplifies to:
\[ b = 10 \]

7. **Conclusion**:
- Therefore, the number of blue balls in the bag is \( 10 \).

### Final Answer:
The number of blue balls in the bag is \( 10 \).

---