Question

72b384 is a number in which one of its digits is ‘b'. If the number is a multiple of 9, what is the numerical value of ‘b'?

Answer 1

A number is divisible by 9 if and only if the sum of its digits is divisible by 9.

So, the sum of the digits of your number is

$7+2+b+3+8+4 = 24+b$

Since b ranges from 0 to 9 (it is a digit and it can't have any other values), 24+b ranges from 24 to 33. The only multiple of 9 in this range is 27, which we obtain by choosing b=3.

So, the only way to choose a value for b in order to make your number divisible by 9 is choosing b=3 and thus getting the number 723384, and indeed we have

$\dfrac{723384}{9}=80376$