math

A positive two-digits number is such that the product of the digits is 24.When the digits are reversed,the number formed is greater than the original number by 18.Find the number

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  1. let the unit digit be x
    and the tens digit by y
    then the original number is 10y + x
    and the number reversed is 10x + y

    10x + y - (10y + x) = 18
    9x - 9y = 18
    x - y = 2
    but we also know that xy = 24

    it should be obvious that the two number are 6 and 4.
    Since reversing the numbers made the number bigger, the original must have been 46

    check:
    6x4 = 24 , that's good
    original = 46
    reversed = 64
    64 - 46 = 18 , all is good!

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  2. Let the digits be xy,x is the ones digit& y tens digit.Hence;
    Xy=24---(i)
    (X+10y)-(y+10x)=24---(ii)
    (ii)
    X+10y-y-10x
    X-10x+10y-y
    -9x+9y=18
    9y-9x=18
    Y-x=2--(ii)
    but;xy=24
    X=2+y
    Y(2+y)=24
    Y'2+2y-24=0
    Product=-24
    Sum=2
    Numbers 6,-4
    Since digits were(+)ignore the(-)sign
    Product of digits xy;6×4=24,terrific
    Therefore;
    Original number=46
    New number=64

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