I am a two-digit number. Dividing me by the sum of my digits yields a quotient of 7 with no remainder. If you subtract 27 from me, my digits switch places. What number am I?
63
Let the number be 10a + b. First condition: 10a + b = 7(a + b) implies 3a = 6b, so a = 2b. Second condition: (10a + b) - 27 = 10b + a simplifies to 9(a - b) = 27, so a - b = 3. Substituting a = 2b gives 2b - b = 3, so b = 3 and a = 6. The number is 63.
About this riddle
Math riddles hide a calculation inside a short story. Pull out the numbers, work out what is being asked, and watch for a trick such as a unit change.
Difficulty: Hard. More like this: Math riddles with answers or try Target 24 for a different kind of puzzle.
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