Auto: GToooanov A.C.

The sum of the digits in the decimal representation of a natural number $n$ is 100, and the sum of the digits of the number $44 n$ is 800. What is the sum of the digits of the number $3 n$?
Note that $44 n$ is the sum of 4 instances of the number $n$ and 4 instances of the number $10 n$.

If we add these numbers digit by digit, then in each digit place, there will be the sum of the quadrupled digit from the same place in the number $n$ and the quadrupled digit from the next place. If no carries occur in this process, then each digit of the number $n$ is added 8 times, and the sum of the digits in all places is 800. With carries, the sum of the digits obviously decreases (since 10 is subtracted from one place and only 1 is added to another). Therefore, in the situation described in the problem, no carries occur. This means, in particular, that any digit of the number $n$ does not exceed 2. Then, when multiplying $n$ by 3, each of its digits is simply multiplied by 3, and, therefore, the sum of the digits is also multiplied by 3.

Therefore, the sum of the digits of the number 3n is 300.

## Answer

300.00