Find an unknown number

[biggie]

There is an integer whose last digit is 0. We increase this number by 10% and the sum of its digits decreases by 10%. I need to find at least one such number and i am totally stuck.

 

[PA3040D]

If last digit is 0 then number should be multifil by 10 or 100 or .....

 

[Otis]

EDIT: Please disregard this post. I'd misread the word in red as "increases".

an integer whose last digit is 0. We increase this number by 10% and the sum of its digits decreases by 10%

It seems like we can find an example by simply experimenting. I guessed a few random Integers from 5 to 7 digits long, and two of them worked! (I'm not usually lucky, so I'm thinking that there are probably a lot of examples that work.)

Hint: Choose Integers whose sum-of-digits is a multiple of 10.



PS: In both cases that worked for me, the increased sum of digits turned out to be the same number. There could be a pattern.

 

[blamocur]

If the number's last digit is 0 its sum of digits stays the same after dividing by10. But [imath]x*1.1 = (x/10) * 11[/imath], i.e. find numbers whose sum of digits decreases by 10% after multiplying by 11.
Also note that the sum of digits stays integer after being decreased by 10%, i.e. the hint in the post #3.

 

[PA3040D]

There is an integer whose last digit is 0. We increase this number by 10% and the sum of its digits decreases by 10%. I need to find at least one such number and i am totally stuck.

It should be 30 there may be more