A two digit number is such that the product of digit is 8 . when 18 is added to the number , the digits are reversed . The number is:

A two digit number is such that the product of digit is 8 . when 18 is

1.	A two digit number is such that the product of digit is 8 . when 18 is added to the number , the digits are reversed . The number is:
Answer» Let the digits of the number are `x` and `y` where `y` is the unit digit. Then, the number will be `10x+y`. It is given that, ` xy = 8=>x = 8/y->(1)` Also, `10x+y +18 = 10y+x` `=>9x-9y = -18` `=>x-y = -2` `=>8/y - y = -2` `=>8-y^2 = -2y` `=>y^2-2y -8 = 0` `=>y^2-4y+2y -8 = 0` `=>y(y-4)+2(y-4) = 0` `=>(y+2)(y-4) = 0` `=> y = -2 or y = 4` We will take positive value for `y`, that is `4`. `:. x = 8/y = 8/4 = 2` So, the number is `2**10+4 = 24.`

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A two digit number is such that the product of digit is 8 . when 18 is added to the number , the digits are reversed . The number is:

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