Question

in a two digit number the units digit exceeds its tens digit by 2. the product of the given number and the sum of its digits is equal to 144 find the number

Answer 1

let the tens digit be x
therefore unit digit will be x+2
therefore the number Will be 10x+x+2
the sum of the digit = 2x+2
(10x+x+2)(2x+2)=144
(11x+2)2(x+1)=144
(11x+2)(x+1)=72
11x²+11x+2x+2=72
11x²+13x-70=0
-13+-√(169+4×770)/22
-13+-√(169+3080)/22
-13+-√(3249)/22
-13+-57/22
-13+-57/22
and continue further

Answer 2

Answer: The required number is 24.

Step-by-step explanation:  Let (10x + y) be the number, where 'x' is the ten's digit and 'y' is the unit's digit.

According to the given information, we have

$y=x+2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i),\\\\(10x+y)(x+y)=144~~~~~~~~~~~~~(ii).$

Substituting the value of 'y' from equation (i) in equation (ii), we have

$(10x+x+2)(x+x+2)=144\\\\\Rightarrow (11x+2)(2x+2)=144\\\\\Rightarrow 2(11x+2)(x+1)=144\\\\\Rightarrow (11x+2)(x+1)=72\\\\\Rightarrow 11x^2+11x+2x+2=72\\\\\Rightarrow 11x^2+13x-70=0\\\\\Rightarrow 11x^2+35x-22x-72=0\\\\\Rightarrow x(11x+35)-2(11x+35)=0\\\\\Rightarrow (x-2)(11x+35)=0\\\\\Rightarrow x-2=0,~~~~~11x+35=0\\\\\Rightarrow x=2,~~~~~~~x=-\dfrac{35}{2}.$

Since the ten's digit 'x' of the number cannot be a fraction or negative, so x = 2.

Therefore, from equation (i), we get

$y=x+2=2+2=4.$

Thus, the required number is given by

$10x+y=10\times2+4=20+4=24.$