Question

The base ( or radix) of the number system such that the following equation holds 312/20 = 13.1 is
1. 3
2. 4
3. 5
4. 6

Answer 1

Correct Answer - Option 3 : 5

The correct answer is 5

• Let ‘x’ be the base or radix of the number system. The equation is:
  • \(\frac{3x^2 + 1x^1 + 2x^0}{2x^1+ 0x^0}\)    =   \(1x^1 + 3x^0 + 1x^{-1}\)
  • => \(\frac{3x^2 + x + 2}{2x}\)   =   \(x + 3 + \frac{1}{x}\)
  • => \(\frac{3x^2 + x + 2}{2x}\)   =   \(\frac{x^2 + 3x + 1}{x}\)
  • => \(3x^2 + x + 2\)   =   \(2x^2 + 6x + 2\)
  • => \(x^2 - 5x\)   =   0
  • => \(x(x - 5)\)   =   0
  • => \(x = 0 \)   or   \(x = 5\)
• Therefore, x = 5