Question

A number of three digits in the septenary scale is represented in the nonary scale by the same three digits in reverse order; if the middle digit in each case is zero, find the value of the number in the denary scale.

Answer 1

Let the number in septenary scale be $a0b$ and in nonary scale be $b0a$

Now if we convert both of them to denary scale we have,

$49a+b=81b+a\Rightarrow 48a=80b\Rightarrow 3a=5b$

The only single digit number is possible when $a=5$ and $b=3$

Hence, the number in denary scale is $49a+b=248$