the digits of a two digit number differ by 5. if the digits are interchanged and resulting number is added to the orignal , we get 99.​

Question

the digits of a two digit number differ by 5. if the digits are interchanged and resulting number is added to the orignal , we get 99.​

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Savannah 1 week 2021-09-13T20:52:24+00:00 1 Answer 0 views 0

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    2021-09-13T20:53:45+00:00

    Answer:

    Let the digit in ten’s. Place be x and the digit in the one’s place be y.

    ∴x−y=5⟶(i)

    ∴ Two digit number=10x+y

    Two digit after reversing the digits=10y+x

    According to question ,

    ∴10x+y+10y+x=99

    ⇒11x+11y=99

    ⇒x+y=9⟶(ii)

    On adding (i) and (ii),

    2x=14

    ⇒x=7

    Putting the value of x in equation (i)

    x−y=5

    ⇒y=2

    ∴ Number=10x+y

                        =72.

    Step-by-step explanation:

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