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Problem #24 · August 20, 2026

Natural numbers

If the digit 00 is appended to the right of a two-digit number, the number increases by 405405. Find the original number.
  1. A4545
  2. B4040
  3. C4444
  4. D5050
  5. E5454

WORKED EXAMPLE

Solution

Let the original number be xx. When a zero is written to its right, the number becomes 10x10x. By the condition, 10x−x=40510x - x = 405, that is, 9x=4059x = 405, hence x=405:9=45x = 405 : 9 = 45. Check: 450−45=405450 - 45 = 405.
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