A six digit number is divisible by 33. If 54 is added to the number then the new number formed will also be divisible by

Here's why:

A number is divisible by 33 if it is divisible by both 3 and 11 (since 33 is a product of 3 and 11).

1. A number is divisible by 3 if the sum of its digits is divisible by 3. Adding 54 to a number doesn't change this property, because the sum of the digits of 54 (5+4=9) is divisible by 3.

2. A number is divisible by 11 if the difference between the sum of digits at odd places and the sum of digits at even places is either 0 or a number divisible by 11. Adding 54 to a number doesn't change this property, because 54 has only two digits and it will be added to the last two digits of the original number, which doesn't change the difference between the sum of digits at odd places and the sum of digits at even places.

Therefore, if a six-digit number is divisible by 33, adding 54 to the number will result in a new number that is also divisible by 33.