Consider the following equation and find out the base of the number system (radix r):

(143)r = (25)r + (43)r + (11)r + (20)r 

(A) 5
(B) 6
(C) 7
(D) All of the above


Answer: (B)

Explanation: On solving, given equation,

(143)r = (25)r + (43)r + (11)r + (20)r 
r2 + 4r + 3  = 2r + 5 + 4r + 3 + r + 1 + 2r
r2 -5r -6 = 0
(r - 6)*(r + 1) = 0 

Since, value of base (or radix) can not be negative. So,

r = 6 

So, option (B) is correct.


Quiz of this Question