UGC NET CSE | December 2019 | Part 2 | Question: 12

Question

Given following equation:

$(142)_b + (112)_{b-2} = (75)_8$, find base $b$.

• A. $3$
• B. $6$
• C. $7$
• D. $5$

Answer 1

let us convert each of the numbers in base b,(b-2),8 into decimal numbers.

$142_b+112_{b-2}=75_8$

$2+4*b+b^2+2+b-2+(b-2)^2=5+8*7$

$2+4b+b^2+b+b^2+4-4*b=61$

$2b^2+b-55$

From the given options, only b=5 satisfies the above equation.

So it is the answer.