# 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:

1
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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