Given:
- Metallic white balls = 40% of W = 0.40W
- Metallic black balls = 50% of B = 0.50B
- Number of metallic white balls = Number of metallic black balls
- Total number of balls = 450
Step 1: Equating metallic balls
Since metallic white balls = metallic black balls:
\( 0.40W = 0.50B \quad \text{...(i)} \)
Step 2: Total number of balls
\( W + B = 450 \quad \text{...(ii)} \)
Step 3: Express W in terms of B
From equation (i):
\( W = \frac{0.50}{0.40}B = \frac{5}{4}B \quad \text{...(iii)} \)
Step 4: Substitute (iii) in (ii)
\( \frac{5}{4}B + B = 450 \)
\( \Rightarrow \frac{9B}{4} = 450 \)
\( \Rightarrow 9B = 1800 \)
\( \Rightarrow B = 200 \)
Step 5: Find W
\( W = 450 - B = 450 - 200 = 250 \)
Step 6: Calculate metallic and non-metallic balls
- Metallic white balls = \( 0.40 \times 250 = 100 \)
- Metallic black balls = \( 0.50 \times 200 = 100 \)
- Non-metallic white balls = \( 250 - 100 = 150 \)
- Non-metallic black balls = \( 200 - 100 = 100 \)
- Total non-metallic balls = 150 + 100 = 250
Final Answer: 250 non-metallic balls