Question

In a two digit, if it is known that its units digit exceeds its tens 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: EXPLAINED ANSWER

Answer 1

Let the digit at tens place be x and at ones place be y

The required number is 10x+y

According to question,
y=x+2
And, (10x+y)(x+y)=144
(10x+x+2)(x+x+2)=144
(11x+2)(2x+2)=144
22x²+26x-140=0
(x-2)(11x+35)=0
x=2
and y=x+2=2+2=4

The required number is 24