Question

the sum of two digit number is 12 and the number obtained by interchanging its digit exceeds the given number by 18 find the number

Answer 1

Let the digit at ten's place be x.

Let the digit at one's place be y.

Therefore the required two digit number = 10x + y.

The number obtained by interchanging the digits = 10y + x.

Given that sum of two digit number = 12.

x + y = 12   ------ (1)


Given that number obtained by interchanging its digits exceeds the given number by 18.

10y + x = 10x + y + 18

9x - 9y = 18

x - y = 2   ----- (2)


On solving (1) & (2), we get

x + y = 12

x - y = 2

--------------

 2x = 10

x = 5.


Substitute x = 5 in (1), we get

x + y = 12

5 + y = 12

y = 12 - 5

y = 7.


Therefore the original number = 57.

 

Hope this helps!

Answer 2

Hello,

Let us assume x and y are the two digits of the number

Therefore, two-digit number is 

10x + y 

and the reversed number:

10y + x

Given:

x + y = 12

y = 12 – x                (1)

Also given:

10y + x - 10x – y = 18

9y – 9x = 18

y – x = 2                    (2)

Substitute the value of y from (1) in (2)

12 – x – x = 2

12 – 2x = 2

2x = 10

x = 5

Therefore, y = 12 – x = 12 – 5 = 7

Therefore, the two-digit number is:
10x + y = (10×5) + 7 =50+7= 57

bye :-)