the sum of the digits of a two digit number is 12 if the new number formed by reversing the digit is greater than the original number by 18

Question

the sum of the digits of a two digit number is 12 if the new number formed by reversing the digit is greater than the original number by 18 find the original number check your solution​

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Lydia 3 weeks 2021-09-06T05:33:59+00:00 1 Answer 0 views 0

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    2021-09-06T05:35:07+00:00

    Step-by-step explanation:

    Let x be the unit digit and y be tens digit.

    Then the original number be 10x+y.

    Value of the number with reversed digits is 10y+x.

    As per question, we have

    x+y=12 ….(1)

    If the digits are reversed, the digits is greater than the original number by 18.

    Therefore, 10y+x=10x+y+18

    ⇒9x−9y=−18 ….(2)

    Multiply equation (1) by 9, we get

    9x+9y=108 ….(3)

    Add equations (2)and (3),

    18x=90

    ⇒x=5

    Substitute this value in equation (1), we get

    5+y=12⇒y=7

    Therefore, the original number is 10x+y=10×5+7=57..

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