A boy contains 15 white and some black balls. If the probability of drawing a black ball from the bag is thrice that of drawing a white ball, find the number of black balls in the bag.

Answer

To solve the problem, we need to find the number of black balls in the bag given that the probability of drawing a black ball is three times that of drawing a white ball. Let's denote the number of black balls as \( b \).

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Number of white balls = 15
- Number of black balls = \( b \) (unknown)
- Probability of drawing a black ball is three times the probability of drawing a white ball.

2. **Calculate Total Number of Balls:**
- Total number of balls = Number of white balls + Number of black balls
\[ \text{Total balls} = 15 + b \]

3. **Calculate the Probability of Drawing a White Ball:**
- The probability of drawing a white ball is given by:
\[ P(\text{White}) = \frac{\text{Number of white balls}}{\text{Total number of balls}} = \frac{15}{15 + b} \]

4. **Calculate the Probability of Drawing a Black Ball:**
- The probability of drawing a black ball is given by:
\[ P(\text{Black}) = \frac{\text{Number of black balls}}{\text{Total number of balls}} = \frac{b}{15 + b} \]

5. **Set Up the Equation Based on the Given Condition:**
- According to the problem, the probability of drawing a black ball is three times that of drawing a white ball:
\[ P(\text{Black}) = 3 \times P(\text{White}) \]
Substituting the probabilities we calculated:
\[ \frac{b}{15 + b} = 3 \times \frac{15}{15 + b} \]

6. **Simplify the Equation:**
- Cross-multiplying gives:
\[ b = 3 \times 15 \]
\[ b = 45 \]

7. **Conclusion:**
- The number of black balls in the bag is \( b = 45 \).

### Final Answer:
The number of black balls in the bag is **45**.