MathematicsThe sum of two-digit numbers and the number obtained by reversing the order of the digit is 121. Find the number, if the digits differ by 3.

The sum of two-digit numbers and the number obtained by reversing the order of the digit is 121. Find the number, if the digits differ by 3.


  1. A
    47 or 74
  2. B
    36 or 63
  3. C
    67 or 76
  4. D
    94 or 49  

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    Solution:

    Given, the sum of two-digit numbers and the number obtained by reversing the order of the digit is 121.
    The digits differ by 3.
    Let the two digit number be 10x+y.
    On reversing its digits, we get,
    The number 10y+x.
    ⇒ (10x+y)+(10y+x)=121 ⇒ 11x+11y=121 ⇒ x+y=11 …  (1) Also,
     x-y=3 … (2) Adding equations (1) and (2), we get.
    ⇒ 2x=14
    ⇒ x=7 Substituting x=7 in the equation (2), we get,
    ⇒ 7-y=3
    ⇒ y=4 Hence, the number is 74 or 47.
    Hence, the correct option is 1.
     
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