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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

Let’s draw the table for better understanding.

$$\begin{array}{|l|ccc|} \hline & \textbf{Black} & \textbf{White} & \\\hline \text{Metallic} & x & x & \\ \text{Non-metallic} & x & 1.5x & \\ \text{Total} & 2x & 2.5x & 450 \\\hline \end{array}$$
Now, $2x+2.5x = 450$

$\Rightarrow 4.5x = 450$

$\Rightarrow \boxed{x = 100}$

$\therefore$ The number of non-metallic balls $\text{(Black+White)}= x+1.5x = 2.5x = 2.5 \times 100 = 250.$

Correct Answer : $250$
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