Skip to main content
PPrime
← Back to archive

Problem #68 · October 3, 2026

Natural numbers

If the digits of a two-digit number are swapped, the number increases by 2727. Find the original number if the sum of its digits is 99.
  1. A2727
  2. B3636
  3. C4545
  4. D5454
  5. E6363

WORKED EXAMPLE

Solution

Let the number be ab‾=10a+b\overline{ab} = 10a + b. When the digits are swapped, (10b+a)−(10a+b)=9(b−a)=27(10b + a) - (10a + b) = 9(b - a) = 27, hence b−a=3b - a = 3. Solving this together with a+b=9a + b = 9 gives b=6b = 6, a=3a = 3, so the original number is 3636; check: 63−36=2763 - 36 = 27.
Solve today's problem