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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
The base ( or radix) of the number system such that the following equation holds $\dfrac{312}{20}=13.1$ is
Solution
Base (Radix) Problem Solution
Question: Find the base r such that
(312)r ÷ (20)r = (13.1)r
Expansion in base 10
- (312)r = 3r² + 1r + 2
- (20)r = 2r
- (13.1)r = r + 3 + 1/r
Equation
(3r² + r + 2) / (2r) = r + 3 + 1/r
Multiply both sides by 2r
3r² + r + 2 = 2r² + 6r + 2
Simplification
r² - 5r = 0
⇒ r(r - 5) = 0
✅ Final Answer
Since base must be > 1, the valid solution is:
Base (radix) = 5
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Commented Oct 17 , 2023
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