📢 Too many exams? Don’t know which one suits you best? Book Your Free Expert 👉 call Now!
  • google app store apple app store
    • ✖

      Question

      When the digits of a two-digit number are interchanged,

      the new number becomes 39 less than 150% of the original number. If the sum of the digits is 6, find the original number.
      A 24 Correct Answer Incorrect Answer
      B 33 Correct Answer Incorrect Answer
      C 42 Correct Answer Incorrect Answer
      D 51 Correct Answer Incorrect Answer
      E 60 Correct Answer Incorrect Answer

      Solution

      Let the unit digit and tens digit of the original number be ‘y’ and ‘x’, respectively.
      Original number = (10x + y)

      According to the data given: 
      10y + x = 1.5 × (10x + y) − 39

      Multiplying both sides by 2, 
      20y + 2x = 30x + 3y − 78 
      ⇒ 28x − 17y = 78  …. (I)

      And, x + y = 6  …. (II)

      From (II), x = 6 − y. Substitute in (I): 
      28(6 − y) − 17y = 78 
      168 − 45y = 78 
      45y = 90 
      y = 2

      Then x = 6 − 2 = 4. 
      So, original number = 10 × 4 + 2 = 42.

      Practice Next
      More No. System Questions
      ask-question