Question

In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:

Answer 1

let the tens digit be x then unit digit = x+2
 now a.t.q

(11x+2)(2x+2)=144
22x²+26x+4=144
11x²+13x+2-72=0
11x²+13x-70
11x² 35x-22x -70=
x(11x+35) -2(11x+35)=0
therefor x=2or x=-35/11
since digit can't be negative
x=2
then number is  24