The tens' digit of a two digit number is less by 3 than unit digit. If the product of the two digits is subtracted from the number the result is 15. Find the unit digit of the number.

Explanation

Let the unit digit be x.
`:.` The tens' digit is (x-3)
`:.` the number =10(x-3)+x.
`=10x-30+x=11x-30`.
As per questions, `(11x-30)-x(x-3)=15`.
or, `11x-30-x^(2)+3x=15or,x^(2)-14x+45=0`
or, `x^(2)-(5+9)x+45=0`
or, `x^(2)-5x-9x+45=0`
or, `x(x-5)-9(x-5)=0`
or, `(x-5)(x-9)=0`.
`:.` either `x-5=0" "or,x-9=0`
`impliesx=5" "or,xx=9`.
Hence the unit digit is 5 or 9