Question

A box has 450 balls, each either white or black, there being as many metallic white balls as metallic black balls. If 40% of the white balls and 50% of the black balls are metallic, then the number of non-metallic balls in the box is

Answer 1

Correct Answer: 250

Input Data:

• Metallic white balls constitute 40% of W, represented as \( 0.40W \).
• Metallic black balls constitute 50% of B, represented as \( 0.50B \).
• The quantity of metallic white balls equals the quantity of metallic black balls.
• The aggregate number of balls is 450.

Step 1: Equalization of Metallic Balls

Given that the number of metallic white balls is equal to the number of metallic black balls:
\( 0.40W = 0.50B \quad \text{...(i)} \)

Step 2: Total Ball Count

\( W + B = 450 \quad \text{...(ii)} \)

Step 3: Express W in terms of B

Derivation from equation (i):
\( W = \frac{0.50}{0.40}B = \frac{5}{4}B \quad \text{...(iii)} \)

Step 4: Substitution of (iii) into (ii)

\( \frac{5}{4}B + B = 450 \)
\( \Rightarrow \frac{9B}{4} = 450 \)
\( \Rightarrow 9B = 1800 \)
\( \Rightarrow B = 200 \)

Step 5: Determination of W

\( W = 450 - B = 450 - 200 = 250 \)

Step 6: Calculation of 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

Conclusion: 250 non-metallic balls