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The number obtained by interchanging the two digits of a two-digit number is less than the original number by 45. If the sum of the two digits of the number so obtained is 13, then what is the original number?

Correct answer: B. 94

  • A. 49
  • B. 94
  • C. 83
  • D. Either (a) or (b)
  • E. None of these

Explanation

Let the original number be 10a + b and its reversal 10b + a. Since the reversal is 45 less, 9(a - b) = 45, so a - b = 5; with a + b = 13, the digits are a = 9 and b = 4, giving 94. A likely choice is option a, 49, from selecting the reversed number instead of the original number.

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