A bag contains white and black balls. The ratio of the white and black balls is 4 ∶ 7. If the number of black balls is 280, then find the number of white balls in the bag

Options

A. 120
B. 80
C. 160
D. 200

Answer

To solve the problem, we need to find the number of white balls in the bag given the ratio of white to black balls and the number of black balls.

### Step-by-Step Solution:

1. **Understand the Ratio**: The ratio of white balls to black balls is given as 4:7. This means for every 4 white balls, there are 7 black balls.

2. **Set Up Variables**: Let the number of white balls be represented as \(4x\) and the number of black balls as \(7x\), where \(x\) is a common multiplier.

3. **Use the Given Information**: We know that the number of black balls is 280. Therefore, we can set up the equation:
\[ 7x = 280 \]

4. **Solve for \(x\)**: To find the value of \(x\), divide both sides of the equation by 7:
\[ x = \frac{280}{7} = 40 \]

5. **Calculate the Number of White Balls**: Now that we have \(x\), we can find the number of white balls:
\[ \text{Number of white balls} = 4x = 4 \times 40 = 160 \]

6. **Conclusion**: The number of white balls in the bag is 160.

### Final Answer:
The number of white balls in the bag is **160**.