If the number 59a44b is divisible by 36, then the maximum value of a + b is:

a and b are digits of the number

$$=$$>  $$0\le a\le9$$  and  $$0\le b\le9$$

$$=$$>  $$0\le a+b\le18$$ .................(1)

Given, the number 59a44b is divisible by 36

$$=$$>  The number 59a44b is divisible by 9

If a number is divisible by 9 then the sum of the digits of the number is divisible by 9

$$=$$>  5+9+a+4+4+b is divisible by 9

$$=$$>  22+a+b is divisible by 9 .........(2)

From (1) and (2), the possible values of a+b = 5,14

$$\therefore\ $$The maximum value of a+b = 14

Hence, the correct answer is Option B