A box contains 12 green balls and some red balls. If the probability of drawing a red ball from the box is twice that of drawing a green ball, then find the number of red balls in the box.

Options

A. 20
B. 18
C. 24
D. 15

Answer

To solve the problem, we need to find the number of red balls in the box given that the probability of drawing a red ball is twice that of drawing a green ball.

### Step-by-Step Solution:

1. **Define Variables:**
Let the number of red balls be \( N \). We know there are 12 green balls.

2. **Calculate Total Balls:**
The total number of balls in the box is the sum of green and red balls:
\[ \text{Total balls} = 12 + N \]

3. **Calculate Probabilities:**
- The probability of drawing a red ball \( P(R) \) is given by:
\[ P(R) = \frac{N}{12 + N} \]
- The probability of drawing a green ball \( P(G) \) is given by:
\[ P(G) = \frac{12}{12 + N} \]

4. **Set Up the Equation:**
According to the problem, the probability of drawing a red ball is twice that of drawing a green ball:
\[ P(R) = 2 \times P(G) \]
Substituting the expressions for \( P(R) \) and \( P(G) \):
\[ \frac{N}{12 + N} = 2 \times \frac{12}{12 + N} \]

5. **Simplify the Equation:**
Since both sides have the same denominator, we can multiply both sides by \( 12 + N \) (assuming \( 12 + N \neq 0 \)):
\[ N = 2 \times 12 \]
This simplifies to:
\[ N = 24 \]

6. **Conclusion:**
The number of red balls in the box is \( N = 24 \).

### Final Answer:
The number of red balls in the box is **24**.