The sum of two numbers is equal to 495. The last digit of one of them is zero. If you cross the zero off the first number you will get the second. What are the numbers?

To answer this item, we let x be the hundreds digit of the first number, and y be the tens digit. This makes the first number equal to,

      100x + 10y 

The second number then equals 10x + y. 

Since the last digit of the sum is equal to 5 then,

     0 + y = 5

Hence,

     (100x + 50) + (10x + 5) = 495

Simplifying,
      110x + 55 = 495

The value of x from the equation is 4. 

Hence, the numbers are 450 and 45.