A three-digit number N (in decimal) contains the digit 0. When the zero is removed, the resulting number is exactly N/9. What is the value of N?
Note: The number may contain more than one zero. The number may not begin with a zero.
+310 We have two options to consider: If the 0 that is removed is the middle digit or if 0 is the last digit.
Case 1: N=a0b
10a+b=(100a+b)/9
90a+9b=100a+b
8b=10a
4b=5a
b=5, a=4
Case 2: N=ab0
10a+b=(100a+10b)/9
90a+9b=100a+10b
10a=-b
The only answer for this is when a and b equal 0. But this number isn't a valid three digit number.
So our answer is 405
