In The Search of Number for '?'

Here is the question! 

First two equations clearly indicates it must be straightforward a + b equation.

Now if you observe closely all the equations, then you can find that the number never exceeds 8. So there are chances that all these number are in octal number system i.e. base 8 numbers.

Hence 11 in third equation is actually 8 in decimal. That's why 7 + 8 = 15 where decimal 15 is converted to octal 17. 

Verifying third equation as 15 + 16 = 31 in decimal is actually 17 + 20 = 37.

On the similar note, we have fourth equation in decimal as 31 + 32 = 63 which can be converted to octal as 37 + 40 = 77.

Hence the search for number in place of '?' ends with the number 77.