Question

The sum of the digit of a two digit number is twelve if 18 is added to it the digits are reversed.find the number

Answer 1

x+y=12

in tens place =y
in units =x
.

no. is 10 y+x

reverse =10x+y

eq 10 y+x +18 = 10 x+y
-9x +9y +18=0. .......1
x+y=12 .......2
9(x+y =12)
9x+9y = 108
add .........
18 y=126
y = 7
putting y in 1 eq x=5

Answer 2

Answer:

let \: the \: ones \: digit \:  = x \\ and \: tens \: digit \:  = y \\ so \: the \: number \:  = 10y + x \\ according \: to \: question \: x + y = 8..........(1) \\ and \: if \: added \: 18 \: the \: number \:  =>  10y + x  + 18 = 10x + y \\  = > 9y - 9x =  - 18 \\  => 9x - 9y = 18..........(2) \\ (1) \times 9 => 9x + 9y = 72........(3) \\ (3) - (2) => 18y = 54 \\ so \: y = 3 \\ and \: from \: (1) \: x = 5 \\ hence \: the \: number \: is \:  = 10y + x = 10 \times 3 + 5 = 35

Step-by-step explanation: