Question

The sum of the digits of a two digit number is 12. The number obtained by reversing the digits is 36 greater than the original number. Find the number.

Answer 1

$Let \: us \: assume \: x \: and \: y \: are \: the \: two \: digits \: of \: the \: number \\ Sum \: of \: the \: digit \: is \: 12 \: \\ x+y=12 \: \: \: \: \: ......(1) \\ Original \: Number \: = 10x+y \\ according \: to \: the \: question \\ 10y+x=10x+y+36 \\ 9(y-x)=36 \\ y-x=4 \: \: \: \: \: \: \: ........(2) \\ Add \:equ.(1) and\: equ.(2) \\ 2y=16 \\ y=8 \\ put \: the \: value \: in \: equation(1) \: we \: get \\ x + 8 = 12 \\ x = 12 - 8 \\ x=4 \\ Original \: Number \: = 10x + y = 10 (4 )+ 8 = 48$

Answer 2

The sum of the digit of the two digit number is 12. When the digit are interchange, the result number is 36 more than the original number. What is the original number?

Let the unit digit=X

Tens digit=12-X

The number=10(12-X)+X

The number after reversal=10(X)+12-X

The equation

10(12-X)+X-36 =10X+12-X

120–10X+X-36=10X+12-X

-10X+X-10X+X=12–120–36

-18X=-144

18X=144

X=144/18

X=8x

X=unit digit=8

Tens digit=12–8=4

The number=10(4)+8=48

Reverse number=84

84 is 36 more than 48

So the desired number is 48