Question

The sum of the digit of two digit number is 12. The number obtained by interchanging the digits exceeds the given number by 18. Find the number

Answer 1

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 eqn 1 in eqn 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 = 57

Answer 2

Let the digit in the number is xy.

So number is 10x + y

Given

sum of the digits of a two-digit number is 12

=> x+ y = 12..........................1

Again

10y + x = 10x+ y +18

=> 10y + x - 10x - y = 18

=> 9y -9x = 18

=> y - x = 2 ..................2

Solving equation 1 and 2, we get

x = 5, y = 7

So the number is 57.