White and black metallic balls

CAT 2021 Slot 2 · QA · Easy · Percentages

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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

250

Explanation

Let WW be the total number of white balls and BB be the total number of black balls. W+B=450W + B = 450.

Metallic white balls = 0.4W0.4W. Metallic black balls = 0.5B0.5B.

Given 0.4W=0.5B  ⟹  4W=5B  ⟹  W=54B0.4W = 0.5B \implies 4W = 5B \implies W = \frac{5}{4}B.

Substituting WW: 54B+B=450  ⟹  94B=450  ⟹  B=200\frac{5}{4}B + B = 450 \implies \frac{9}{4}B = 450 \implies B = 200 W=250W = 250

Metallic white balls = 0.4×250=1000.4 \times 250 = 100. Metallic black balls = 0.5×200=1000.5 \times 200 = 100. Total metallic balls = 100+100=200100 + 100 = 200.

Number of non-metallic balls = 450−200=250450 - 200 = 250.

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