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reyesjanearie
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Tyro
Asked: 2021-04-07T08:51:55+00:00 In:

QUESTION OF THE DAY 04/07/21

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The sum of the 2-digit number is 8. If the digits are reversed, the number is 36 more than the original number. Find the number

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  1. acedstud
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    Let the tens digit be a and the ones/units digit be b, then the number is given by 10\times a+1\times b=10a+b.

    “The sum of the 2-digit number is 8” means a+b=8 . . . . . (1).

    If the digits are reversed, then b becomes the tens digit and a becomes the ones/units digit and the new number becomes 10\times b+1\times a=10b+a.

    When the digits are reversed, “the new number is 36 more than the original number” means 10b+a=36+10a+b\Rightarrow-9a+9b=36 . . . . . (2).

    Dividing (2) through by 9 gives -a+b=4 . . . . . (3)

    Adding (1) and (3) gives (a+b)+(-a+b)=8+4\Rightarrow a+b-a+b=12\Rightarrow2b=12\Rightarrow b=\dfrac{12}{2}=6.

    From (1), a+b=8\Rightarrow a+6=8\Rightarrow a=8-6=2.

    Therefore, the original number is 10a+b=10(2)+6=20+6=26, while the new number is 62.

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