Question

sum of the digits of a two digit number is 12 . the given number exceeds the number obtained by interchanging the digit by 36 . find the given number ​

Answer 1

Answer:

The given number ​is 84.

Step-by-step explanation:

Let one's digit be x.  

Then, ten's digit $=12-x$

      Number

                             $=10(12-x)+x\\ \\ =120-10x+x\\ \\ =120-9x$

Number obtained by reversing the digits

                                                 $=10(x)+12-x\\ \\ =12+9x$

According to the given condition, we have  

                                 $120-9x=12+9x+36\\ \\ 120-12-36=9x+9x\\ \\ 72=18x\\ \\ x=4$

So, the number =120−9x=120−9×4=120−36=84

Answer 2

Answer : The Given number is 84

Step-by-step explanation :

Given : sum of digits of a two digit number = 12

The given number exceeds the number obtained by interchanging

the digit by 36.

To find : The given number = ?

Let,

sum of the digit = x+y -----------(1)

interchanging number = (10x+y) - (10y+x) = 36

(10x+y)-(10x+y) = 36

10x + y - 10x - 10y = 36

9x - 9y = 36

9( x - y ) = 36

( x - y )=36/9

x - y = 4 ---------------(2)

Adding equation 1 and 2

x + y + x - y = 12 + 4

2x = 16

x = 16/2 = 8

x = 8

Putting the value of x = 8 in equation (1)

We get,

8 + y = 12

y = 12 - 8

y = 4

∵ 10x + y = the required number

Substituting the value of x and y

We get ,

10 × 8 + 4 = 84