NIMCET 2016 Question Paper with solutions

Question : 49 of 120

Marks: +1, -0

Consider the equation

(43)_x

(y3)_8

where x and y are unknown. The number of possible solutions is;

Solution:

Given,

(43)_x=(y3)_8

By converting to decimal system

4x^{1}+3x^{0}=y⋅8^{1}+3⋅8^{0}

4x+3=8y+3

4x=8y

x=2y

x is the base of number system x > 4
y is number in the number system with base 8, so y < 8

Number of possible solutions = 5

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