The base ( or radix) of the number system such that the following equation holds 312/20 = 13.1 is
In base b: \(312_b = 3b^2 + b + 2\), \(20_b = 2b\), and \(13.1_b = b + 3 + \frac{1}{b}\).
\(2b\left(b + 3 + \frac{1}{b}\right) = 2b^2 + 6b + 2 = 3b^2 + b + 2\)
\(b^2 - 5b = 0 \Rightarrow b = 5\)
Answer: (C) 5
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