Question

What is the ratio A: B where A represents 6 Zero’s concatenated to the rightmost digit of a positive integer of base 8 and B represents 5 Zero’s concatenated to the rightmost digit of a positive integer of base 8. (Write your answer in the space provided up to 2 decimal places)___

Answer 1

Let the number be $(xy{)}_n=nx+y$
If we concatenate one zero at the rightmost digit it becomes
$(xy0{)}_n=n^{2}x+yn$
= n(nx+y) [which is equal to n times the number]
Now concatenate two zeros at the rightmost digit of the number.$\Rightarrow (xy00{)}_n=n^{3}x+y^{2}n$
$=n^2(nx+y)$
Similarly if we concatenate 60’s it becomes $n^6(nx+y)$
$\therefore$ Required Ratio $=\frac{\left(n^6\right(nx+y)}{\left(n^5\right(nx+y)}=n$
Base is 8, Hence the Required answer is 8.00