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Home Aptitude Linear Equation See What Others Are Saying!
  • Question
  • The number obtained by interchanging the two digits of a two-digit number is lesser than the original number by 54. If the sum of the two-digit number is 10, then what is the original number?


  • Options
  • A. 28
  • B. 39
  • C. 82
  • D. cannot be determined

  • Correct Answer
  • 82 

    Explanation

    Let us assume the digits of the original number are unit's digit a and ten's digit b.
    The Original Number will be 10a + b.
    After interchanging the digits the new number will be 10b + a.
    According to question,
    The number obtained by interchanging the two digits of a two-digit number is lesser than the original number by 54.
    New Number = Original Number - 54
    10b + a = 10a + b - 54
    ? 10b + a - 10a - b = -54
    ? 9b - 9a = -54
    ? a - b = 6....................................(1)
    Again according to question,
    Sum of the digits of original number = 10
    a + b = 10..................................................(2)
    Add the equation (1) and (2), we will get
    a - b + a + b = 10 + 6
    2a = 16
    a = 8
    Put the value of a in Equation (2) , we will get
    8 + b = 10
    b = 10 - 8
    b = 2
    Put the value of a and b for original number, we will get
    10a + b = 10 x 8 + 2 = 80 + 2 = 82


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